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Optimal political control of the bureaucracy.

It is widely believed that insulating an administrative agency from the influence of elected officials, whatever its other benefits or justifications, reduces the agency's responsiveness to the preferences of political majorities. This Article argues, to the contrary, that a moderate degree of bureaucratic insulation from political control alleviates rather than exacerbates the countermajoritarian problems inherent in bureaucratic policymaking. An elected politician, though responsive to majoritarian preferences, will almost always deviate from the majority in one direction or the other. Therefore, even if the average policy position of a given elected official tends to track the policy views of the median voter in the electorate, the average divergence between the preferences of that official and the median voter in the electorate is generally greater than zero. Forcing the politically responsive official to share power with a partially insulated bureaucracy can reduce the variance in policy outcomes, because bureaucratic insulation creates a kind of compensatory inertia that mutes the significance of variation in the elected official's policy preferences. Up to a point, the median voter's benefit from this reduction in outcome variance outweighs the costs associated with biasing the expected outcome away from the median voter's ideal policy.
TABLE OF CONTENTS

INTRODUCTION
  I. THE CONVENTIONAL WISDOM
 II. ANALYSIS
     A. Assumptions
        1. The Normative Standard
        2. The Positive Framework
     B. The Baseline Analysis
        1. Optimal Bureaucratic Insulation at the
           Policymaking Stage
        2. Optimal Bureaucratic Insulation at the
           Institutional Design Stage
     C. Extensions
        1. Voter Internalization of Presidential Control Costs
        2. Voter Monitoring and Lobbying of the President.
        3. Strategic Voter Selection of a Biased President
        4. Extended Policy Time Horizon
CONCLUSION
APPENDIX
       A. Players and Order of Play
       B. Equilibrium Strategies
          1. Equilibrium Strategy of the Bureaucracy
             and the President
          2. Optimal Bureaucratic Insulation in the
             Policymaking Stage
          3. Optimal Bureaucratic Insulation in the Institutional
             Design Stage
      C. Extensions
         1. Social Costs of Bureaucratic Control Efforts
         2. Alternate Methods of Accountability
         3. Strategic Voter Selection of Biased Presidents
         4. Longer Time Horizons


INTRODUCTION

The degree to which elected politicians ought to influence bureaucratic policymaking is one of the most important and contested questions in public law. A prominent school of thought--endorsed by influential scholars, practitioners, and public servants--maintains that increasing political influence over the bureaucracy enhances the majoritarian legitimacy of the administrative state, while insulation of the bureaucracy from political control (whatever its other benefits or justifications) is necessarily "countermajoritarian" and therefore problematic. This conclusion is supported by a simple, powerful, and intuitive argument: most bureaucratic policy choices involve fundamentally political value trade-offs, and in a democracy there is a strong presumption that such choices should reflect the interests of electoral majorities. Elected politicians--for example, the president--tend to respond to majoritarian interests; appointed bureaucrats are much less responsive. It therefore seems self-evident that giving politicians greater influence over agencies, all else equal, will always increase the degree to which agency decisions reflect majoritarian preferences.

This Article argues that this seemingly obvious conclusion is false: a moderate degree of bureaucratic insulation alleviates rather than exacerbates the countermajoritarian problems inherent in bureaucratic policymaking. Even if elected politicians are more responsive to voters than are agencies, and even if agencies do not have any special expertise or other advantages, a majority of the electorate is still better off with some degree of bureaucratic insulation from political control. The reason has to do with the fact that an elected politician, though responsive to majoritarian preferences, will almost always deviate from the majority in one direction or the other. Republican presidents, for example, are almost always more conservative than a majority of the electorate, while Democratic presidents are typically more liberal. So even if the average policy position of presidential administrations tends to track the policy views of the median voter in the electorate, the average divergence between the preferences of the median voter and the president is generally greater than zero. Forcing the politically responsive president to share power with a partially insulated, politically unresponsive bureaucracy tends to reduce the variance in policy outcomes, because bureaucratic insulation creates a kind of compensatory inertia that mutes the significance of variation in the president's policy preferences. Up to a point, the benefit to a majority of voters from a reduction in outcome variance outweighs the cost associated with biasing the expected outcome away from the median voter's ideal outcome. A majority of voters therefore prefers a moderate level of bureaucratic insulation from political control.

This result contrasts sharply with the received wisdom that majoritarian values are best served by maximizing the degree to which politically responsive elected officials can control unaccountable bureaucrats. It is important to stress, though, that the optimal level of bureaucratic insulation has the expected relationship with other political and institutional variables. The more responsive an elected politician is to majoritarian preferences, the lower the majority's optimal level of bureaucratic insulation. Likewise, the greater the bureaucracy's expected policy bias, the lower the optimal level of bureaucratic insulation. And the more voter preferences tend to shift over time--or, equivalently, the more serving a majority's interests may require sudden and dramatic policy changes--the lower the optimal level of bureaucratic insulation. These comparative results, however, do not alter the fact that, except in special cases, the optimal level of bureaucratic insulation will be positive.

This Article develops the central argument and several extensions using a positive political theory ("PPT") framework. Part I surveys existing scholarship. With very few exceptions, the conventional wisdom is that if one presumes that (1) politicians are responsive to majoritarian preferences, (2) bureaucrats are not, (3) bureaucrats do not have special expertise or other advantages that would be undermined by greater political control, and (4) responsiveness to majoritarian preferences is the only relevant normative criterion, then elected politicians should have maximum influence over bureaucratic policymaking, except in special circumstances. Part II, the heart of the Article, assesses this conventional wisdom using a stylized PPT framework. Section II.A lays out the normative and positive assumptions that structure this analysis. Section II.B derives the optimal degree of bureaucratic insulation under these assumptions. This analysis establishes the main result: except in special cases, majoritarian values are best served by a degree of bureaucratic insulation from political control. Because this baseline analysis incorporates a number of strong simplifying assumptions, Section II.C considers several extensions. These variants generate additional insights, but they do not substantially undermine the central claim that political majorities often prefer to limit the influence of accountable politicians over unaccountable bureaucrats. A technical appendix presents the formal model on which the analysis and conclusions in the body of the Article are based.

I. THE CONVENTIONAL WISDOM

Many distinguished scholars and practitioners believe that it is illegitimate and undesirable for bureaucrats to pursue policy goals that diverge from those of the nation's elected representatives. Over thirty years ago, Lloyd Cutler and David Johnson concisely summarized this view by defining a "regulatory failure" as a situation in which "an agency has not done what elected officials would have done had they exercised the power conferred on them by virtue of their ultimate political responsibility." (1) In other words, agencies fail "when they reach substantive policy decisions ... that do not coincide with what the politically accountable branches of government would have done if they possessed the time, the information, and the will to make such decisions." (2) This definition of bureaucratic failure rests on two premises, one normative and the other positive. The normative premise is that regulatory policy should be maximally responsive to the preferences of a majority of the electorate. The positive premise is that the best way to assure bureaucratic responsiveness to majoritarian preferences is to make agency policy choices as responsive as possible to the preferences of the elected political leadership.

The normative premise that democratic institutions should generally maximize majoritarian responsiveness is vulnerable to a variety of criticisms, including the claims that one cannot ascribe coherent preferences to a collective body, (3) that majoritarianism may actually reduce aggregate voter welfare, (4) and that political institutions should advance normative goals other than satisfaction of the preferences of current electoral majorities. (5) This Article brackets these objections and provisionally assumes, consistent with much of the existing literature advocating extensive political control of the bureaucracy, that majoritarianism is a legitimate and coherent institutional goal.

What about the positive premise--that if majoritarianism is our objective, we should confer as much authority as possible on politically accountable elected officials? The notion that one can increase the political responsiveness of bureaucratic decisions by increasing the influence of the most politically responsive decision maker commands widespread acceptance. Richard Pierce, for example, states that political control over agency decisions is desirable because "[p]olicy decisions should be made by the most politically accountable institution available." (6) Similarly, Peter Strauss and Cass Sunstein assert that "[f]or those who believe that regulatory issues present questions to be resolved 'politically'--in accordance with (informed) constituent desires--decisionmaking power should be placed in the hands of those most accountable to the public." (7)

Of course, most political-control advocates concede that it is too costly to eliminate bureaucratic insulation completely. The fact that elected officials have limited time and expertise, for example, may make some de facto bureaucratic autonomy inevitable. (8) Furthermore, aggressive political monitoring that deprives agencies of policymaking autonomy may erode agency incentives to invest in expertise, thereby raising the costs to elected politicians of acquiring policy-relevant information. (9) These informational considerations may induce even committed majoritarians to tolerate some degree of bureaucratic autonomy. But this "agency slack" is viewed as acceptable only if the costs (to majoritarian interests) of bringing the bureaucracy to heel are too high. Furthermore, these informational arguments do not necessarily undermine the claim that majoritiarian interests are best served by giving politicians maximum authority over bureaucratic policy, because the politicians themselves may choose to give agencies a degree of autonomy if doing so would serve majoritarian interests.

Scholars have also identified special circumstances in which the satisfaction of majoritarian preferences may require a degree of bureaucratic independence from political control. For example, a time-consistency problem, also known as a credible commitment problem, may provide a majoritarian justification for insulating central banks, the judiciary, and some public utility commissions from direct political control. (10) Some level of bureaucratic insulation may also improve voter welfare by reducing political risk. (11) Additionally, the insulation of certain institutions--such as courts or legislative districting commissions--may be important for ensuring that elected politicians remain sufficiently responsive to majoritarian interests. (12) But these are special cases. For the mine-run of bureaucratic policy decisions--from environmental protection to workplace safety to criminal prosecution to food and drug regulation--the conventional view is that giving maximum authority to the most politically responsive decision maker maximizes the responsiveness of policy to majoritarian preferences.

This general view may imply a variety of legal and institutional conclusions. Some believe that the need to put politically accountable officials in charge of bureaucratic policy demands a revitalization of the nondelegation doctrine. On this view, Congress is too eager to delegate authority to unaccountable bureaucrats who cater to narrow interests rather than broad majorities. According to nondelegation advocates, if Congress could not transfer responsibility for making fundamental policy decisions, Congress would make more of these decisions through the legislative process and would be held accountable for its choices. (13) The plausibility of this claim has been vigorously challenged, (14) and the strong form of the nondelegation view has virtually no traction under current doctrine. (15) Nonetheless, arguments that emphasize Congress's relatively greater majoritarian responsiveness may provide support for the judicial application of "nondelegation canons" of statutory construction. (16) Moreover, some scholars have suggested that administrative procedures and interpretive default rules can and should increase the control of the current Congress over regulatory policy, even--or perhaps especially--if broad delegations are considered legitimate. (17)

Proponents of strong presidential control over the administration also argue for maximum feasible political responsiveness in bureaucratic policymaking. Scholars with diverse ideological and methodological commitments have asserted that the two premises discussed above--that bureaucratic policy should track majoritarian values and that this goal is best advanced by giving decision-making authority to the most politically accountable officials--imply the need for presidential control over bureaucratic policymaking, because the president is the institutional actor most responsive to the preferences of a national majority. Lawrence Lessig and Cass Sunstein, for example, posit that presidential control over the bureaucracy is necessary to serve the constitutional commitment to political accountability because, "to the extent that an agency official makes discretionary decisions about the content of public policy, the best reading of the constitutional plan is that in general, the official may not be insulated from presidential supervision." (18) Putting Lessig and Sunstein's constitutional views to one side, numerous other experts agree that the political responsiveness of bureaucratic policy to the preferences of the national electorate correlates strongly with presidential control of the administration. In addition to Lessig and Sunstein, prominent proponents of this hypothesis include James Blumstein, (19) Steven Calabresi, (20) Philip Hatter, (21) Elena Kagan, (22) Jerry Mashaw, (23) Richard Pierce, (24) and Peter Strauss. (25)

Some of those who support strong presidentialism on majoritarian grounds believe that the Constitution, sound institutional-design principles, or both require a "unitary executive" in which the president has complete authority over all aspects of the administration. (26) Other strong presidentialists do not take their conclusions quite this far, but this is not because they reject the premise that presidential control maximizes the political responsiveness of bureaucratic policy. Rather the allowance for some degree of bureaucratic insulation from the president is a concession to values other than majoritarian responsiveness. Elena Kagan is explicit about this. After noting that individuals and institutions other than the president (including interest groups, congressional committees, and the agencies themselves) have a "far more tenuous connection to national majoritarian preferences and interests," Kagan nonetheless allows that these entities "may have important roles to play and contributions to make in the administrative process." (27) But, she explains, this is only because "responsiveness to the general electorate is not the sole criterion by which to assess administrative action." (28) On the dimension of political responsiveness to the electorate, Kagan is unequivocal that "the President holds the comparative advantage." (29) Thus she concludes that, "given the current ubiquity of broad delegations, [democratic] values support the strongest feasible presidential control of administrative decisions." (30) Strauss and Sunstein take a similar approach. They acknowledge a need to maintain "tension" between the "neutral expertise" and "political" views of regulation, (31) and they admit some role for the former in shaping procedural constraints on the president's authority to direct the administration. That said, Strauss and Sunstein are quite clear that on the dimension of political responsiveness, presidential control over the bureaucracy is always a benefit. (32) The implication is that the more one cares about majoritarianism, the more one ought to favor presidential control over the administration.

The view that increasing presidential control over the administration would increase the political responsiveness of agency policy may imply a variety of legal or institutional arrangements that reduce bureaucratic insulation from the president, at least to the extent this can be done without excessive erosion of other relevant values (such as bureaucratic competence or fairness). (33) Versions of the majoritarian responsiveness argument have been used to justify, for example, deferential judicial review of agency action on questions of both law (34) and policy; (35) conditioning such deference on evidence that the president or her immediate subordinates were involved in making the relevant decision; (36) allowing agencies to change their policies easily in response to a new president's political priorities; (37) imposition of centralized regulatory review through the Office of Management and Budget ("OMB"); (38) allowing the president to issue policy directives to agencies; (39) shifting the authority within the executive branch to interpret statutes from the agencies to the Department of Justice ("DOJ"); (40) increasing the power of White House representatives within agencies; (41) and restricting Congress's ability to limit the president's removal authority or to delegate to officials not under the president's direct control. (42)

The enthusiasm for presidential control of the administration, however, is far from universal. Indeed the critics of strong presidentialism may outnumber the proponents. Yet an interesting feature of the varied and vociferous criticisms of strong presidentialism is that few, if any, reject the notion that placing decision-making authority with the most politically responsive officials will increase the majoritarian responsiveness of the decisions themselves. Instead, critiques of strong presidentialism tend to make one or both of two other claims.

First, many critics assert the priority of other values, such as "rule of law," "procedural regularity," or "rationality," over majoritarian responsiveness. (43) Lisa Bressman, for example, has argued that excessive attention to political accountability has obscured the importance of preventing arbitrary agency decision making. (44) Furthermore, these critics sometimes assert that the type of direct responsiveness that strong presidentialists attribute to the chief executive can pose a threat to important public values other than majoritarianism. (45) These criticisms, however, do not directly undermine the hypothesis that the majoritarian responsiveness of bureaucratic policy correlates positively with the influence of politically accountable elected officials. Rather, these critics posit that the costs of presidential control, in terms of damage to other values, outweigh whatever majoritarian benefits presidential control might confer.

Second, many critics dispute the claim that the president is more politically responsive than other institutions to national majorities. Some argue that greater presidential control over the administration might actually threaten majoritarian values by eroding the influence of Congress, which arguably has even stronger majoritarian credentials than the president, (46) or by undermining an administrative process that does, or could do, a reasonably good job of responding to voter preferences. (47) These concerns are exacerbated by the lack of transparency associated with some forms of presidential control. (48) Whatever the validity of these criticisms, however, none of them rejects the premise that increasing the authority of the most majoritarian decision makers over the bureaucracy will increase the majoritarian responsiveness of bureaucratic decisions. Indeed the preceding criticisms are not targeted at the political responsiveness theory per se, but rather at its strong presidentialist variant.

In sum, the conventional majoritarian case for strong presidentialism rests on three premises: (1) political and legal institutions should increase the responsiveness of bureaucratic policy to the values held by a majority of voters, (2) increasing the relative influence of the most politically accountable entities over the bureaucracy will increase the majoritarian responsiveness of bureaucratic policy, and (3) of our existing institutions, the president is the most responsive to majoritarian preferences. Critics of strong presidentialism have attacked the first and third premises, but for the most part they have left the second intact. Part II of this Article develops a simple theoretical framework to assess the idea that maximizing the power of the institution most responsive to majoritiarian preferences in fact maximizes the majoritarian responsiveness of bureaucratic decisions. The analysis concludes that this hypothesis is at best seriously incomplete and at worst flat-out wrong.

II. ANALYSIS

A. Assumptions

1. The Normative Standard

One problem afflicting much of the literature that invokes the concepts of "political responsiveness," "political accountability," and "political representativeness" is that these malleable terms are not always clearly defined. (49) This Article adopts a simple, functional definition of political responsiveness and treats the closely related concepts of political accountability and political representativeness as synonymous. (50) For the purposes of this Article, "political responsiveness" is the degree of correspondence between the policy the bureaucracy implements and the policy that a majority of the electorate would select if the issue were put to a vote.

More specifically, the analysis assumes that the policy outcome (which can be interpreted as a single decision or as the aggregate effect of multiple decisions) can be characterized as a point in a one-dimensional space (that is, a line). For convenience, one might think of the line as capturing a traditional left-right (liberal-conservative) policy continuum, but the dimension could be anything. The preferences of a majority of the national electorate can be represented, in abstracted form, as the preferences of a single median voter (referred to simply as the "voter") with a most-preferred outcome (an "ideal point") in the policy space. The voter's utility is a decreasing function of the distance between the policy outcome and the voter's ideal point. The degree of "expected policy responsiveness" is simply the expected distance between the policy outcome and the voter's ideal point. (51)

The following analysis uses expected policy responsiveness as the exclusive normative criterion to judge different institutional arrangements. This is not because policy responsiveness is the only value that legal and political institutions ought to respect, but rather because this Article focuses on how well different institutional arrangements serve majoritarian values. Because much of the case for strong presidentialism (or political control of the bureaucracy more generally) rests on claims about advancing majoritiarian responsiveness, it makes sense to put that case on its strongest footing by temporarily excluding consideration of other values.

It is worth noting, however, that the following analysis could proceed in exactly the same way if what I refer to as the "voter's ideal point" were redefined as something other than the median voter's most preferred policy. For example, one could define this point as the policy that maximizes aggregate voter welfare, the policy that most closely approximates what the policy outcome would have been under the original understanding of the Constitution's decision-making process, or some other definition of the "optimal democratic outcome." As long as the positive assumptions outlined in the next subsection hold, the main substantive conclusions will also hold. While little in the analysis depends on identifying the optimal democratic outcome with the median voter's ideal point, this identity is often made or assumed in discussions of the appropriate degree of political control over agencies, and so I will use this terminology for expositional convenience.

2. The Positive Framework

This Article considers a stylized model of bureaucratic policymaking that includes two, and only two, government decision makers: an elected politician, referred to as the president, and an unelected bureaucracy. It is important to emphasize that the decision to label the elected politician the "president" is purely for expositional convenience. The analytical framework would apply in exactly the same way if this actor were labeled "Congress" or "Congress-plus-the-president." (52)

The model divides the decision-making process into two stages: an "institutional design stage" and a "policymaking stage." (53) In the institutional design stage, two important events occur. First, a bureaucracy is created. The bureaucracy's initial ideal point may diverge from the voter's initial ideal point by some amount, and the magnitude of this distance is the "initial bureaucratic bias." (54) Second, institutional rules are established, and these rules determine the degree of "bureaucratic insulation" from presidential control. (55)

At the beginning of the policymaking stage, the voter's ideal point may shift some amount to the left or right; neither direction is more likely ex ante. Although the analysis assumes that institutional designers do not know which direction voter preferences will shift, or exactly how much, the expected magnitude of the shift is known at the institutional design stage. We can use the term "voter preference instability" to characterize the expected magnitude of the voter's preference shift. When voter preferences are stable, shifts are likely to be relatively small; when voter preferences are unstable, shifts are likely to be relatively large. (56) This feature of the model allows assessment of the claim that political control over the bureaucracy is necessary to respond to changes in the voter preferences. (57)

After the voter settles on a new ideal point, the political process determines the president's ideal point. The president is politically responsive to the electorate in the sense that the president's (induced) policy preferences are positively correlated with the voter's preferences. More precisely, the expected value of the president's ideal point is equal to the voter's ideal point, and if the voter's ideal point shifts, the expected value of the president's ideal point shifts as well. (58) Presidential responsiveness to majoritiarian preferences may arise because voters select presidents on the basis of the candidates' perceived values and interests, because sitting presidents cater to the preferences of the electorate, or both. (59)

Although the expected value of the president's ideal point is always equal to the voter's ideal point, there is no guarantee that the president's actual ideal point will match the voter's ideal point exactly. Indeed, the president's actual ideal point is likely to end up some distance to the left or right of the voter's. After all, no system of political accountability works perfectly, and even the most ardent proponents of strong presidentialism concede that the president's policy goals may diverge somewhat from those of the median voter. (60) But these presidential deviations from voter preferences can be treated as a kind of random error, or "noise," in the political process. As Steven Calebresi argues, "the exigencies of the business cycle almost guarantee that both of the two major parties will share the Presidency, at least to some degree. This means that relatively permanent minority positions on various issues will always enjoy periods where presidential power is friendly and periods where it is not." (61) From this observation, Calebresi concludes that although "some presidents may temporarily become out of touch on [particular regulatory] issues[,] ... over time these divergences will tend to cancel each other out, producing long term accountability." (62)

We can characterize the average size of the deviation between the president's ideal point and the voter's ideal point as "expected presidential responsiveness." (63) When expected presidential responsiveness is high, the set of likely presidential ideal points is clustered tightly around the voter's ideal point. When expected presidential responsiveness is low, the set of likely presidential ideal points is more widely dispersed. In all cases, the probability-weighted average of the possible presidential ideal points is equal to the voter's ideal point.

In contrast to the president's ideal point, voter preferences do not directly affect the bureaucracy's ideal point. Left to its own devices, the bureaucracy will continue to pursue the same policy. This assumption, while unrealistically strong, captures in stylized form the claim--common in the literature advocating greater political control--that bureaucracies suffer from a kind of inertia or "arteriosclerosis" that leads them to hew to a particular policy agenda unless prodded from the outside. (64) Furthermore, the analysis could easily be extended to incorporate the possibility that bureaucratic policy preferences might be subject to random variation. All one would need to do is to redefine the parameter that measures the expected random change in the difference between voter preferences and bureaucratic preferences from "voter preference instability" to something broader that captures both voter preference shifts and bureaucratic preference shifts. (65) For simplicity, however, the rest of the discussion will proceed under the assumption that the bureaucracy's initial ideal point is fixed.

While bureaucratic policy preferences are not directly responsive to voter interests, the president--who is responsive to voter interests, at least in expectation--has a number of tools at her disposal to shift the bureaucracy's ideal point. These tools include the power to appoint and remove administrative officials, to manipulate bureaucratic structure and procedures, to impose various forms of regulatory review, and to issue directives to agencies, as well as a variety of other, less formal means. The specific tools the president might use are not important here. Rather, the important consideration is that it is costly for the president to employ them. This cost is typically not a direct expenditure of material resources but instead the opportunity cost of the president's time, attention, and political capital.

The president's control cost is proportional to two things: the distance the president moves the bureaucracy's ideal point and the level of bureaucratic insulation from presidential influence. All else equal, it is more costly for the president to effect a large change in bureaucratic preferences than to effect a small change. Holding the size of the change constant, the president incurs greater control costs when the bureaucracy is more insulated from political control. Furthermore, the president's marginal cost of influencing the bureaucracy increases as the size of the policy change becomes larger. That is, the cost to the president of moving the bureaucracy two units in a given direction is more than twice as large as the cost to the president of moving the bureaucracy one unit in that direction. (66)

The assumption of increasing marginal control costs is important to the subsequent results, so it is worth pausing to explain its justification. This assumption is premised on the notions that bureaucratic control costs are primarily opportunity costs--the diversion of time, effort, and political capital from other activities--and that the president tries to allocate these resources efficiently, sacrificing low-value activities before high-value activities. Imagine, for purposes of illustration, that the president has 100 units of political capital that she allocates to an array of tasks. If the president devotes a single unit of capital to influence a particular bureaucratic decision (so the president devotes 1 unit to bureaucratic control and 99 to other tasks), she will sacrifice whichever other activity was least valuable to her; to do otherwise would be irrational. The value of that foregone activity is the cost of devoting 1 unit of political capital to bureaucratic control. Now suppose the president devotes a second unit of political capital to bureaucratic control (so that she applies 2 units to bureaucratic control and 98 units to other tasks.) (67) Because the president has already foregone the lowest-valued of her original set of alternative activities, the opportunity cost of devoting this second unit of political capital to bureaucratic control will be higher than the opportunity cost of the first unit. Hence, the cost to the president of devoting 2 units of political capital to bureaucratic control is more than twice as great as the cost of devoting 1 unit to bureaucratic control. As long as the president rationally sacrifices low-value activities before high-value activities, then the marginal cost to the president of influencing the bureaucracy is increasing in the distance the president moves the bureaucracy's ideal point. (68)

Finally, after the president has altered the bureaucracy's preferences, the bureaucracy implements its (new) ideal policy. The benefits of this policy choice to the president and to the voter are inversely proportional to the distance between this policy and the ideal points of the president and the voter, respectively. (69)

B. The Baseline Analysis

We can now address this Article's central question: What is the optimal level of bureaucratic insulation from political control? Section II.B.1 considers what the answer to this question would be at the policymaking stage, when the ideal points of the president, the bureaucracy, and the voter are all known. The more interesting and important case, however, is when the level of bureaucratic insulation must be established at the institutional design stage. Section II.B.2 analyzes this case and demonstrates that the optimal level of bureaucratic insulation is always positive, except in the unrealistic special case where the president is perfectly responsive to voter preferences. This result contrasts with the widely held view that if majoritarianism is the only relevant normative consideration, the politically responsive president should have unfettered control of the administration. As a comparative matter, however, the results of the analysis in Section II.B.2 are consistent with intuitive hypotheses about the relationship between optimal bureaucratic insulation and other political-institutional variables: The optimal level of bureaucratic insulation is negatively correlated with expected presidential responsiveness, initial bureaucratic bias, and voter preference instability.

1. Optimal Bureaucratic Insulation at the Policymaking Stage

Consider first the optimal level of bureaucratic insulation at the policymaking stage, when the ideal points of the voter, president, and bureaucracy are all known with certainty. (70) For expositional convenience, assume that before the president exerts any influence, the bureaucracy's ideal point is located to the right of the voter's ideal point. (71) There are three cases to consider, each of which is depicted in Figure 1.

[FIGURE 1 OMITTED]

First, if the president is even further to the fight of the voter than the bureaucracy (Case 1 in Figure 1), the voter prefers the bureaucracy to be completely insulated from presidential control. In this case, if the president had any influence over the bureaucracy, she would use it to move the bureaucracy even further to the right, away from the voter's ideal point.

Second, if the president is in between the voter and the bureaucracy (Case 2 in Figure 1), the voter prefers the president to have total control over bureaucratic policy. Any leftward move by the bureaucracy in the direction of the president's ideal point is a gain for the voter, so the voter would like to give the president the power to move the bureaucracy as much as the president would like.

Finally, if the bureaucracy is to the voter's right and the president is to the voter's left (Case 3 in Figure 1), the voter prefers an intermediate level of bureaucratic insulation. More precisely, the voter prefers a level of bureaucratic insulation such that, when the president balances the costs and benefits of shifting the bureaucracy's ideal point to the left, the president pulls the bureaucracy just to the voter's ideal point and then stops. If bureaucratic insulation were weaker than this optimal intermediate level, the president would pull the bureaucracy even farther to the left, past the voter's ideal point. If bureaucratic insulation were stronger, the president would shift the bureaucracy's ideal point by a smaller amount, leaving the bureaucracy to the voter's right. If the level of bureaucratic insulation is just right, however, the voter will end up with her ideal policy.

Although this analysis is straightforward, it has notable substantive implications. The voter prefers maximum presidential control only in the limited set of cases where the president's ideal point happens to lie between the voter and the bureaucracy (Case 2 in Figure 1). Otherwise the voter prefers at least some degree of bureaucratic insulation. In other words, if we use "liberal" and "conservative" to denote positions relative to the voter rather than on some absolute scale, the voter only prefers maximum presidential control when a conservative president wants to move a conservative bureaucracy in a liberal direction, or when a liberal president wants to move a liberal bureaucracy in a conservative direction. We should therefore expect the greatest voter support for presidential authority when the president is acting, in a loose sense, against ideological type. (72)

2. Optimal Bureaucratic Insulation at the Institutional Design Stage

The preceding discussion of optimal bureaucratic insulation at the policymaking stage is helpful for building intuition, but the more interesting question concerns the optimal level of bureaucratic insulation at the institutional design stage. (73) How much control would the voter like to give the president over the bureaucracy if the voter must make this choice before she knows for certain what her own preferences, or those of the president, will be in the policymaking stage?

Recall that the expected value of the president's ideal point is always equal to the voter's ideal point. Sometimes the president may be to the voter's left, and sometimes the president may be to the voter's right, but political accountability mechanisms ensure that on average the president's ideal point will equal the voter's. The expected value of the bureaucracy's ideal point, however, may be systematically biased away from the voter. And, in contrast to the president, the bureaucracy's preferences are unaffected by shifts in voter preferences. For these reasons, it is tempting to conclude--along with many strong presidentialists--that at the institutional design stage, the voter is always better off with minimum bureaucratic insulation and maximum presidential control.

That conclusion, however, is fundamentally incorrect. It rests on the fallacious belief that the expected value of the distance between two variables is equal to the distance between the expected values of those two variables. But this is not the case. To illustrate the point with a fanciful example, imagine an archery competition in which each competitor wants to come as close as possible to the bull's-eye. One contestant's shots are "unbiased" but inaccurate: half the time he misses by ten inches to the left, and half the time he misses by ten inches to the right. The second contestant's shots are "biased" but more accurate: her shots always land exactly two inches to the right of the bull's-eye. The expected location of the first archer's shot is the bull's-eye, while the expected location of the second archer's shot is two inches to the right. But what we care about is the expected distance between the shot and the bull's-eye, not the distance between the expected location of the shot and the bull's-eye. For the first archer, this expected distance is ten inches; for the second archer, it is two inches. In this example, and in the context of bureaucratic policymaking, errors to one side or the other do not "cancel each other out."

Even though bureaucratic insulation may bias the expected bureaucratic policy outcome away from the voter's ideal point, bureaucratic insulation may also reduce the variance in policy outcomes. Higher levels of bureaucratic insulation always shift the policy outcome from the president's ideal point toward the bureaucracy's original ideal point. The absolute magnitude of the shift, moreover, is greater for presidents whose policy views diverge substantially from those of the bureaucracy than it is for presidents with preferences relatively close to those of the bureaucracy. The reason is that increases in bureaucratic insulation increase the president's marginal control costs by a constant proportion. Because the president's marginal control costs are an increasing function of the distance the president shifts the bureaucracy's policy preferences, an increase in bureaucratic insulation causes a greater absolute increase in marginal control costs for large shifts in bureaucratic preferences than for small shifts.

This phenomenon is illustrated in Figure 2. This figure depicts a situation in which the bureaucracy's initial ideal point is assumed to be zero. Imagine, for example, that the policy issue is the number of expected cancer deaths per year that would occur in some industry at different levels of regulatory stringency. The bureaucracy, the Occupational Safety and Health Administration ("OSHA") in this example, is assumed to be very aggressive: left to its own devices, it would prefer reducing the number of cancer deaths to zero, even if this would have very high economic costs. The figure then compares graphically the expected final policy outcomes under two possible presidents and two different possible levels of bureaucratic insulation.

[FIGURE 2 OMITTED]

One possible president (let us say the Republican) would prefer a more forgiving regulatory standard that results in two expected cancer deaths per year in the industry. The solid line further to the top right in Figure 2 depicts the Republican president's marginal benefit from moving the final outcome away from OSHA's stringent initial position in the direction of the president's ideal regulation. The president's marginal benefit of moving the policy outcome to the right is positive for any final outcome less than two cancer deaths per year, but this marginal benefit is declining. Another possible president (let us say the Democrat) also views OSHA's initial ideal policy as too stringent, but the Democrat would prefer a moderate level of regulatory stringency that results in one expected cancer death per year. The Democrat's marginal benefit from changing the policy outcome, depicted by the solid line further to the bottom left in Figure 2, is positive but decreasing for any move to the fight up to her ideal point; further moves to the right would imply a negative marginal utility (not depicted in the figure).

The president's marginal cost of moving OSHA's policy to the fight is an increasing function of the size of the policy shift, and the rate at which this marginal cost increases depends on the level of bureaucratic insulation. (74) Figure 2 depicts the president's marginal cost curve at two possible levels of bureaucratic insulation. The lower dashed line in the figure depicts the president's marginal cost at a relatively low level of bureaucratic insulation. The point at which this marginal cost curve intersects the relevant marginal benefit curve determines the expected policy outcomes under Republican and Democratic presidents at this level of bureaucratic insulation. In the example depicted in the figure, these outcomes are 4/3 expected deaths for the Republican and 2/3 expected deaths for the Democrat.

The upper dashed line in Figure 2 represents the president's marginal control cost curve when OSHA is more insulated from presidential control. The president's marginal control cost under this level of bureaucratic insulation is twice as high as the marginal control cost under the level of insulation depicted by the lower marginal cost curve. But this proportional increase in marginal control costs leads to a disproportionate change in the policy outcomes under each president. Again, each president in equilibrium will choose a final policy outcome that equalizes marginal benefits and marginal costs (i.e. the point where her marginal benefit and cost curves intersect). Under the higher level of bureaucratic insulation, this calculation produces a final outcome of 1/2 under the Democrat and 1 under the Republican. For both the Democrat and the Republican, the higher level of bureaucratic insulation shifts the final policy outcome to the left, closer to OSHA's initial ideal point. But the magnitude of this shift is twice as large for the Republican (1/3) as for the Democrat (1/6). This specific example illustrates a more general phenomenon: the greater the distance between the president's ideal point and the bureaucracy's initial ideal point, the greater the sensitivity of the outcome to the level of bureaucratic insulation. As a result, increasing the level of bureaucratic insulation leads to a "compression" of the probability distribution over expected policy outcomes.

Figure 3 provides a graphic illustration of this compression effect, under different assumptions about the probable location of the president's ideal point. In the example depicted in Figure 3, the president's ideal point is drawn from a normal distribution (a bell curve), with the mean of the distribution equal to the voter's ideal point. The dashed curve in Figure 3 depicts this distribution. (75) The bureaucracy, on the other hand, has an ideal point that is fixed some distance to the right of the voter's ideal point.

If the president has total control over bureaucratic policy, then the probability distribution of the final policy outcome is identical to the probability distribution of the president's ideal point (the dashed curve in Figure 3). If the bureaucracy has complete autonomy from the president, the final policy outcome will simply be equal to the bureaucracy's initial ideal point. If the bureaucracy is partially insulated--in the example depicted in the figure, if the level of bureaucratic insulation is such that the president will only move the bureaucracy half as far as she would if she had total control--then solid curve in Figure 3 depicts the probability distribution over the final outcome. Observe that this distribution is biased away from the voter's ideal point: its expected value is halfway between the voter's ideal point and the bureaucracy's initial ideal point. But the distribution is compressed: it has a lower variance than the probability distribution over outcomes when the president has total control. If the level of bureaucratic insulation were higher, the probability distribution of policy outcomes would be centered further to the fight and more compressed; if the level of bureaucratic insulation were lower, this distribution would be centered further to the left and less compressed.

[FIGURE 3 OMITTED]

This compression effect means that the expected divergence between the voter's ideal point and the policy outcome may be lower with a positive level of bureaucratic insulation than with absolute presidential control. To illustrate, consider another example. Imagine that an administrative agency--say, the Environmental Protection Agency ("EPA")--must set an ambient air quality standard, expressed as a maximum allowable concentration level for some pollutant. Setting this standard requires making a difficult trade-off between public health and economic growth. Suppose that the median voter, if fully informed, would prefer a maximum allowable concentration for this pollutant of 0.10 parts per million (ppm). For simplicity, assume that the voter wants to minimize the divergence between the policy outcome and her ideal policy, and assume that she treats deviations above and below her most preferred standard as equally bad.

The EPA prefers a much more aggressive policy: absent external political influence, the EPA would set a maximum allowable concentration of 0.02 ppm. The president is responsive to the median voter's preferences in expectation, but not perfectly so. Let us assume that the president will strive for a maximum concentration of somewhere between 0.03 and 0.17 ppm, with any value in that range equally likely ex ante. Thus the expected value of the president's ideal point is 0.10 ppm, exactly equal to the median voter's ideal point. The expected deviation between the president's ideal point and the voter's ideal point, however, is 0.035 ppm. If an institutional designer interested in maximizing responsiveness to majoritarian preferences had to choose between total bureaucratic autonomy and total presidential control, she would choose the latter. The divergence between the policy outcome and the median voter's ideal point under complete bureaucratic autonomy is 0.08 ppm--more than twice as large as the expected divergence of 0.035 ppm under absolute presidential control.

But the voter might do even better if the EPA is partially insulated from presidential control, so that it is costly but not impossible for the president to influence agency policy. Suppose that, due to some combination of institutional structures, legal rules, and informal norms, each president would find it worthwhile to shift EPA policy only a fraction of the way toward her most-preferred policy. As discussed above, the more distant the president is from the EPA's initial ideal point, the greater the absolute effect of a change in the level of bureaucratic insulation on the policy outcome. Thus increasing the level of presidential influence over the EPA simultaneously shifts the expected outcome away from the EPA's initial ideal point (0.02 ppm) toward the president's expected ideal point (0.10 ppm) and expands the range of possible outcomes from certainty of the EPA's original ideal outcome (0.02 ppm) to the full range of possibilities associated with different possible administrations (from 0.03 to 0.17). These effects are depicted graphically in Figure 4.

[FIGURE 4 OMITTED]

The solid lines in Figure 4 indicate the most stringent and lenient environmental standards that one could expect under different levels of bureaucratic insulation. In other words, these are the outcomes we would observe, for different levels of presidential influence over the bureaucracy, when the president's true ideal point is 0.03 ppm or 0.17 ppm. Because of the assumption that any presidential ideal point in this range is equally likely, the expected outcome under different levels of bureaucratic insulation (depicted by the dashed line in Figure 4) is simply the average of the most extreme possible outcomes. As the level of presidential influence increases (that is, as the level of bureaucratic insulation decreases), the expected outcome shifts from the EPA's initial ideal point (0.02 ppm) to the voter's ideal point (0.10 ppm), but the variance of the possible outcomes (that is, the gap between the most stringent possible outcome and the most lenient possible outcome) also increases.

Because the voter cares about the expected divergence between the actual outcome and her ideal point, the voter may prefer a moderate level of bureaucratic insulation. In the above example, suppose that the EPA is sufficiently insulated that the president would only shift the EPA three-quarters of the way toward her ideal policy. In this case, the distribution of possible policy outcomes will be between 0.0275 ppm and 0.1325 ppm, with any value in that range equally likely. The expected outcome is in that case is approximately 0.08 ppm--too low from the median voter's perspective. But the expected divergence between the outcome and the voter's ideal point in this case is just slightly above 0.03 ppm. This expected divergence is about 14% lower than the expected divergence under absolute presidential control (0.035 ppm). (76) Thus making bureaucratic control somewhat difficult for the president better serves majoritarian values than giving the president absolute control--even though the president's policy preferences reflect the voter's preferences in expectation, and even though the bureaucracy is biased and not directly responsive to voter preferences. (77) The degree of expected policy responsiveness to voter preferences under different levels of presidential influence is illustrated graphically in Figure 5.

[FIGURE 5 OMITTED]

We can illustrate the same general point using another example, with somewhat different assumptions about expected presidential preferences. Suppose that the DOJ must decide how much of its enforcement budget to devote to immigration cases. Suppose further that the median voter, if fully informed, would prefer that the DOJ allocate 3% of its budget to this task. The career staff at the DOJ, however, cares less about immigration than does the median voter: left on its own, the DOJ would allocate only 2% of its budget to immigration enforcement. Now suppose that the president is responsive to voter preferences in expectation but ideological differences cause the priorities of the different parties to skew in different directions. A Democratic president would prefer to allocate only 1% of the DOJ budget to immigration cases, while a Republican president's preferred allocation would be 5%. Finally, assume that the probability that each party wins the presidency is 50%. Figure 6 charts the outcomes under different levels of presidential control over DOJ enforcement priorities, with the actual outcomes under Republican and Democratic presidents given by the upper and lower solid lines, respectively, and the ex ante expected outcome given by the dashed line.

[FIGURE 6 OMITTED]

Under these assumptions, if the median voter had to choose between absolute bureaucratic autonomy and absolute presidential control, she would actually prefer the former. Even though the expected value of the president's ideal point is equal to the voter's, the expected divergence between the voter's ideal policy and the actual outcome is smaller under absolute agency independence (one percentage point rather than two percentage points). The median voter would be even better off, however, if she could give the president some influence over DOJ enforcement priorities but make the exercise of this influence sufficiently costly that the president would not shift DOJ policy as far as she would otherwise prefer. In particular, suppose that a moderate level of bureaucratic insulation means that the president will only shift DOJ policy one-third as far as she would like. If so, then under a Republican president the DOJ will end up allocating 3% of its budget to immigration cases--exactly what the median voter prefers--while under a Democratic president, the allocation will be approximately 1.67%, which the median voter views as too low by approximately 1.33%. Because the ex ante probability that each party wins the presidency is 50%, the expected divergence between the median voter's preferred allocation and the actual outcome is approximately 0.67%. This is better than the 1% divergence the voter could expect from a completely independent DOJ and much better than the 2% divergence the voter could expect from absolute presidential control of DOJ enforcement priorities. Figure 7 illustrates this result.

[FIGURE 7 OMITTED]

These examples are highly stylized, but they illustrate a general theoretical finding with great practical significance: majoritarian interests are often best served not by maximizing the influence of an electorally accountable politician but rather by ensuring a degree of bureaucratic insulation that makes political control of agencies costly but not impossible. Some positive level of bureaucratic insulation will maximize expected policy responsiveness because bureaucratic insulation creates a kind of compensatory inertia that reduces the impact of random deviations in presidential preferences from the median voter's ideal point, thereby reducing the expected variance in policy outcomes. Up to a point, the benefits of this variance reduction will outweigh the costs. (78)

As one might expect, the optimal level of bureaucratic insulation is smaller when expected presidential responsiveness to voter preferences is greater and when initial bureaucratic bias is larger. Optimal bureaucratic insulation is also smaller when voter preferences are unstable. This is because instability in voter preferences increases the expected distance between the voter's ideal point and the bureaucracy's ideal point, but does not affect the expected ideological distance between the voter and the president. (79) Furthermore, this analysis can be extended to consider another of the supposed benefits of strong presidentialism: the president's allegedly greater capacity to respond swiftly to changed conditions, emergent problems, or new information. (80) This consideration is functionally identical to shifts in voter preferences. While the language of "shifting preferences" implies changes in underlying values, the concept could apply just as easily to changing circumstances that call for different policies. Hence the analysis supports the idea that greater presidential control is desirable when voter welfare may require swift policy changes, but it rejects the claim that in uncertain policy environments the (responsive) president should have total control over the (otherwise unresponsive) bureaucracy. In sum, while strong mechanisms of presidential accountability, entrenched bureaucratic bias, and rapidly shifting voter preferences or interests all favor shifting relatively more power to the president, it does not follow that these factors favor maximum presidential control, even if the only normative objective is pleasing a majority of the electorate.

Advocates of strong political control might respond, however, that the median voter's optimal level of bureaucratic insulation, though positive, is likely to be trivially small. If the degree of expected presidential responsiveness to voter preferences is very strong, the bureaucracy's expected bias is severe, or voter preferences are very unstable, then the optimal level of bureaucratic insulation might be low enough that it can be treated as if it were zero, at least for purposes of designing legal doctrines and political institutions. While rigorous empirical testing is beyond the scope of this Article, existing data provide little support for this objection. First, quantitative research shows a consistent and sizable divergence between the views of the median voter in the national electorate and the positions of political parties and presidential administrations. The Republican Party and Republican presidents are notably more conservative than the median voter, while the Democratic Party and Democratic presidents are notably more liberal--though presidents of both parties show responsiveness to changes in voter preferences. (81) This unsurprising finding undermines the notion that the expected distance between the president's agenda and the median voter's ideal point is so small that it can be ignored. (82) Furthermore, while reliable data on bureaucratic bias are scarce, the existing evidence does not support the claim that bureaucratic bias is so extreme that the president's expected divergence from median voter preferences is trivial by comparison. (83) As for voter preference instability, survey research suggests that although voter preferences vary over time, they do not tend to change radically from year to year or election to election. (84)

While none of this is conclusive, these data are broadly consistent with commonsense impressions of U.S. politics: the expected policy agendas of Republican and Democratic presidents diverge from the median voter by nontrivial amounts; agencies, while not directly responsive to the electorate, are not radically out of line with majoritarian preferences; and changes in voter policy preferences are relatively gradual. These observations undermine the claim that the median voter's optimal level of bureaucratic insulation is likely to be so small that it is sensible to treat it as zero for practical purposes. Indeed, if presidents and political parties are relatively polarized, bureaucracies are relatively moderate, and voter preference change is gradual--as some evidence seems to suggest--then the analysis developed in this Article suggests that the optimal degree of bureaucratic insulation from political control may be substantial.

C. Extensions

The analysis in Section II.B.2 establishes a simple hypothesis: the expected responsiveness of bureaucratic policy to voter preferences is maximized when the unaccountable bureaucracy is partially insulated from the politically responsive president. The optimal level of bureaucratic insulation is a decreasing function of expected presidential responsiveness, initial bureaucratic bias, and the instability of voter preferences. Nonetheless the optimal level of bureaucratic insulation is always positive, unless the president is perfectly responsive to voter preferences.

The analysis, however, incorporates a number of strong simplifying assumptions. This Section therefore considers four extensions that address some of the most significant limitations of the baseline analysis. Section II.C.1 explores how the results change if the president's bureaucratic control efforts divert the president from engaging in other activities that affect voter welfare. Section II.C.2 analyzes the case in which the voter can increase expected presidential responsiveness by engaging in costly monitoring and lobbying activities. Section II.C.3 considers a strategic voter who can deliberately bias the president's expected ideal point. Finally, Section II.C.4 extends the policymaking time horizon, considering both cases in which each president's influence over the bureaucracy is temporary and cases in which each president has a more lasting influence over bureaucratic preferences.

1. Voter Internalization of Presidential Control Costs

The baseline analysis assumes that the voter cares about the resources the president devotes to bureaucratic control only because the voter cares about bureaucratic policy outcomes. While this assumption may often be reasonable, it is subject to the following criticism: Influencing an insulated bureaucracy requires the president to divert resources--time, attention, political capital--away from other activities, and some of these alternative uses of presidential resources are likely to affect voter welfare as well as presidential welfare. If so, the voter's expected utility calculations should take into account the degree to which the president's struggles with the bureaucracy divert the president's attention from other tasks. (85)

Incorporating this consideration requires separate analysis of three cases. First, it might be the case that alternative uses of presidential resources confer a positive expected utility on the voter, but the voter cares less about control costs than the president does. This is the most plausible case as a substantive matter. After all, it seems reasonable to suppose that although political accountability mechanisms lead the president to pursue activities that benefit the median voter in most cases, the voter will tend to value the president's alternative projects less than the president does. Second, the voter might value alternative uses of the president's resources more highly than president does. This situation could arise if the president and the voter share the same general objectives, but the president's lowest priorities tend to be the voter's highest priorities. Third, the voter might expect to benefit if the president shifts resources away from alternative projects, if (outside the bureaucratic policy realm) the president tends to pursue activities that harm voter welfare. (86)

Start with the first case, in which presidential control efforts are costly to the voter but less costly than they are to the president. In this case, the voter's optimal level of bureaucratic insulation tends to be pushed toward the extremes. If the optimal level of bureaucratic insulation in the baseline case is low, then increasing the costs to the voter of presidential control will drive the optimal level of bureaucratic insulation even lower. If, on the other hand, the optimal level of bureaucratic insulation in the baseline case is high, then increasing the costliness of presidential control efforts to the voter will push optimal bureaucratic insulation even higher.

The explanation is as follows. When presidential effort is costly to the voter, the voter would prefer less total presidential effort than in the baseline case. Furthermore, the voter would like to reduce presidential effort costs as efficiently as possible. Changing the level of bureaucratic insulation has two effects on presidential effort costs. First, as bureaucratic insulation rises, the president decreases the amount she attempts to shift the bureaucracy's ideal point, which reduces total effort costs. Second, as bureaucratic insulation rises, the marginal cost of shifting the bureaucracy's ideal point goes up, which increases total effort costs. When the voter's optimal level of bureaucratic insulation in the baseline case is high, the former effect predominates: a small change in bureaucratic insulation will lead to a relatively large change in the amount the president shifts the bureaucracy's preferences. Thus an increase in bureaucratic insulation will lead to a net reduction in total control costs. In contrast, when the voter's optimal level of bureaucratic insulation in the baseline case is relatively low, a large change in bureaucratic insulation will lead to only a small change in the amount the president moves the bureaucracy's ideal point. In this case, therefore, reducing bureaucratic insulation will reduce rather than increase total control costs.

Even in this extension, the voter's optimal level of bureaucratic insulation will often remain somewhere between the extremes of total bureaucratic autonomy and total presidential control. It is, however, possible that one or the other of these extremes may be optimal if presidential effort imposes sufficiently high costs on the voter and the optimal level of bureaucratic insulation in the baseline case is already somewhat close to one extreme or the other. By selecting total bureaucratic autonomy or total presidential control, the voter can reduce presidential effort costs to zero. When the president has absolute control of the bureaucracy, she can change the bureaucracy's ideal point as much as she wants without bearing any costs. When the bureaucracy is completely independent, the president does not bother trying to manipulate the bureaucracy's preferences, and so the president does not incur any control costs. Thus there may be situations in which the strong presidentialist thesis holds--but not because unconstrained presidential authority maximizes the expected responsiveness of bureaucratic policy. Rather, the voter sometimes prefers giving the president total control of the bureaucracy, in spite of the fact that doing so makes bureaucratic policy outcomes less responsive to voter preferences, because the voter prefers to free up the president to divert more resources to doing other things the voter cares about.

What about the second case, in which the voter cares as much or more about presidential control costs than does the president herself? In this unusual situation, the voter would prefer either complete bureaucratic autonomy or absolute presidential control; no intermediate level of bureaucratic insulation would ever be optimal. The explanation follows from the earlier discussion. When the voter cares at least as much about the president's control costs as the president does, the voter wants to reduce control costs to zero because expected control costs to the voter always exceed the expected policy benefits the voter might be able to secure from an intermediate level of bureaucratic insulation. Again, the voter has two ways to reduce control costs to zero: either let the president change the bureaucracy's ideal point at no cost or make it impossible for the president to change the bureaucracy's ideal point at all. The voter prefers the former if the optimal level of bureaucratic insulation in the baseline case is low and the latter if the optimal level of bureaucratic insulation in the baseline case is high.

In the preceding two cases, the voter prefers that the president not be "tied down" or "distracted" by struggles with the bureaucracy, all else equal. There might, however, be cases in which the voter is better off if the president is preoccupied trying to rein in the bureaucracy, perhaps because the president will be distracted from doing damage to voter interests in other areas. If so, the basic analysis is the same as in the preceding two cases, but the conclusions are reversed: A voter who benefits from high presidential control costs prefers a more intermediate level of bureaucratic insulation. This both creates strong incentives for the president to exert influence over the bureaucracy and makes the exercise of that influence costly. (87)

2. Voter Monitoring and Lobbying of the President

The baseline analysis treated expected presidential responsiveness to voter preferences as independent of the level of bureaucratic insulation. But if presidential responsiveness to voter preferences is partly a function of how much the voter chooses to invest in monitoring and lobbying the president, this assumption becomes problematic, as voters may consciously increase their monitoring and lobbying activities in response to low bureaucratic insulation. We can address this issue in an extension that assumes the voter can subject the president to either a high level of scrutiny or a low level of scrutiny, where "scrutiny" encompasses a variety of monitoring and lobbying activities that increase the likelihood that the president hews closely to voter preferences. Furthermore, assume that high levels of scrutiny entail greater costs for the voter than low levels of scrutiny, because taking action to increase the political responsiveness of the president diverts voter time, energy, and resources away from other activities. (88)

Incorporating this feature into the analysis leads to the straightforward conclusion that bureaucratic insulation and direct voter scrutiny are partial substitutes. Both greater bureaucratic insulation and higher scrutiny reduce the variance associated with bureaucratic policy outcomes, but both are costly to the voter. When the level of bureaucratic insulation is low, the voter is more likely undertake costly actions to improve presidential accountability. When the bureaucracy is heavily insulated, the voter is less likely to devote scarce resources to scrutinizing the president on the bureaucratic policy issue because the president has less influence over bureaucratic policy outcomes in this case. The voter's optimal level of bureaucratic insulation will be sensitive to this substitution effect. In some cases, the voter prefers a lower level of bureaucratic insulation coupled with stringent scrutiny of the president; in other cases the voter prefers greater bureaucratic insulation and less direct monitoring and lobbying activity.

The fact that bureaucratic insulation weakens voter incentives to engage in activities that promote political responsiveness may seem like an argument against bureaucratic insulation, but this is not necessarily the case if the goal is maximizing voter welfare. Bureaucratic insulation is valuable to the voter precisely because it enables her to shift resources from political monitoring and lobbying to other activities that she values. This observation complicates the claim that greater political control over the bureaucracy is good because it enhances the ability of voters to take action to increase the accountability of elected officials for regulatory decisions. (89) It is true that greater control by elected officials will increase the incentives of voters to monitor these officials and will generally lead to policy outcomes that track the voter's preferences more closely. But from the perspective of voter welfare, these gains may be illusory. The voter might do better by giving the unaccountable bureaucracy somewhat more autonomy and redeploying resources the voter would otherwise have devoted to monitoring and lobbying the president.

3. Strategic Voter Selection of a Biased President

The baseline analysis assumed a particular, and perhaps peculiar, type of presidential responsiveness to voter preferences. In the baseline case, the president's ideal point might diverge some distance to the left or to the right of the voter's ideal point, but expected presidential responsiveness is nonetheless unbiased: the expected value of the president's ideal point is equal to the voter's ideal point. The assumption that expected presidential responsiveness is unbiased suggests that the voter is naive (or, more charitably, sincere) in that she strives simply to select a president who shares her policy preferences. A sophisticated voter, however, might recognize the possibility that she could be better off with a biased president. The degree to which real voters are capable of this sort of strategic thinking is, of course, an open question, the answer to which is likely to depend on context. That said, it is important to explore how the results change under alternative assumptions about voter behavior.

This extension drops the assumption of a naive voter. It assumes instead a sophisticated voter who tries to select a president with the optimal level of bias. (90) This modification yields three related results. First, a rational voter can always neutralize the expected costs of bureaucratic bias by biasing the president's expected ideal point in the opposite direction. Second, the voter's optimal level of presidential bias is greater when the bureaucracy is more insulated from presidential control. Third, and most importantly, when the voter can strategically manipulate the expected presidential bias, the optimal level of bureaucratic insulation is very high. Indeed, if no other considerations are involved, a strategic voter would prefer the highest achievable level of bureaucratic insulation that still allows for the possibility of some presidential influence.

To see the reason for this third result, recall that the main cost of bureaucratic autonomy derives from the bureaucracy's initial bias and its lack of responsiveness to changing voter preferences, while the main cost of presidential control derives from the variance in the president's ideal point. When the voter can strategically manipulate the president's expected bias, she can neutralize the costs of bureaucratic autonomy by selecting a biased president. If the bureaucracy is too far to the left, the voter can try to select a president farther to the right, and vice versa. Absent any constraints on the voter's ability to select the president's expected bias, it does not matter how insulated the bureaucracy is from presidential control as long as some presidential influence is possible. The more insulated the bureaucracy, the more the voter will bias the president, but the end result is the same: the voter can ensure that the expected bureaucratic policy choice is equal to the voter's ideal point. Given this fact, the voter's only concern is with minimizing outcome variance. Because there is variance associated with the president's ideal point, but not the bureaucracy's, the voter would like to minimize the president's influence over policy (without eliminating this influence entirely).

An illustration may help clarify the result. Imagine that the EPA is responsible for setting an ambient air quality standard for some pollutant. Suppose further that the median voter prefers a limit of 0.10 ppm, and the EPA prefers a limit of 0.06 ppm. Political accountability mechanisms work reasonably well, but they are not perfect. The voter can try to select the ideal point of the president, but the president's actual ideal pollution standard may vary by up to 0.04 ppm in either direction, and any value in that range is equally likely. If the president's ideal point were centered on the median voter's ideal point (0.10 ppm), the set of possible presidential ideal points would range from 0.06 ppm to 0.14 ppm. In this case the voter would be best off insulating the bureaucracy such that the president moves the EPA's policy only half as much as the president would like, giving the voter an expected divergence of approximately 0.02 ppm.

But suppose a strategic voter tries to elect a biased president. Suppose, for example, that the voter attempts to elect a president who prefers an extremely lax pollution standard--say 10 ppm, 100 times higher than the median voter's ideal standard. The president's actual ideal point would then be somewhere between 9.96 ppm and 10.04 ppm, with any value in that range equally likely. Suppose further that the EPA is heavily insulated from presidential influence, such that the president will only move EPA policy about 0.42% as far as the president would like. Under these conditions, the expected outcome will be somewhere between approximately 0.098 ppm and 0.102 ppm, with any outcome in this range equally likely. The expected divergence between the policy outcome and the voter's ideal point is only about 0.001 ppm. The voter could do even better if the agency were even more insulated and the president were even more biased.

Taken literally, this result seems to have absurd implications. It suggests, for example, that if a majority of the electorate thought the EPA was slightly too stringent in protecting the environment, the voters would prefer the following strategy: make it extraordinarily difficult for the president to influence EPA policy, and elect a radical anti-environmentalist president. This sort of implausible prediction arises, however, only because the analysis has not incorporated other costs to the voter of increasing expected presidential bias. Such bias may lead to undesirable outcomes on other issues, and it might also decrease expected presidential responsiveness. Furthermore, if the voter internalizes some of the president's control costs, then a system in which a radical president devotes massive resources to influencing an insulated bureaucracy would impose substantial costs on the voter. These considerations mean that even a strategic voter would not want to combine extreme bureaucratic insulation with extreme presidential bias. That said, the basic qualitative result holds even under more realistic assumptions: if the voter selects the president strategically, rather than naively trying to select a president with similar preferences, then the optimal level of bureaucratic insulation is higher than in the baseline case.

4. Extended Policy Time Horizon

The baseline analysis considered only a single policymaking stage. In the real world, however, bureaucratic policy issues can persist for years or decades. While there are a variety of different ways one might think about long-term bureaucratic policy issues, this Section considers a simple extension in which there are two policymaking stages rather than one. At the beginning of the second policymaking stage, voter preferences may shift again; the size of the shift depends on voter preference instability. Next, the voter selects a new president. As in the baseline case, the president is responsive to voter preferences, but not perfectly so--although the expected value of the second president's ideal point is equal to the voter's new ideal point, the new president may deviate by some amount to the right or left. The president then exerts influence over the bureaucracy, and the bureaucracy selects a policy outcome. The level of bureaucratic insulation selected in the institutional design stage persists in both policymaking stages, and the voter wants to maximize the sum of her expected utilities at each stage. (91)

The implications of adding this second policymaking stage depend crucially on whether the president's influence over the bureaucracy's ideal point is temporary or lasting. When presidential influence is temporary, a sitting president can shift the bureaucracy's ideal point--but once the president leaves office, the bureaucracy's ideal point reverts to its initial value. When presidential influence is lasting, each new president takes the bureaucracy as the preceding president left it. (92) In the real world, presidential influence likely has a mix of temporary and lasting effects; for simplicity, the analysis here will treat the cases of temporary and lasting influence as separate ideal types.

In the temporary influence case, optimal bureaucratic insulation is always lower than in the baseline case, and the degree of difference is proportional to voter preference instability. Because voter preferences continue to drift in the second policymaking stage, the expected distance between the voter's ideal point and the bureaucracy's ideal point is higher in the second policymaking stage than in the first. In contrast, because the president's expected ideal point shifts with the voter's, the expected distance between the president and the voter is constant across both stages. When bureaucratic insulation is set at the optimal level, the bureaucracy will be too insulated in the first stage and not insulated enough in the second stage, but the expected sum of the voter's payoffs across both stages will be maximized. Therefore, when there is a second policymaking stage and presidential influence is temporary, the voter prefers to give the president more influence over bureaucratic policy than in the baseline case.

In the lasting influence case, the results are quite different. In some situations, the addition of the second policymaking stage decreases the optimal level of bureaucratic insulation, as in the temporary influence case. In other situations, however, optimal bureaucratic insulation is higher in the lasting influence case than in the baseline case. This latter situation occurs when expected presidential responsiveness is strong relative to initial bureaucratic bias, or when voter preferences are sufficiently stable.

To see the reason for this, recall that after the end of the first policymaking stage, the bureaucracy's new ideal point is a weighted average of the bureaucracy's initial ideal point and the first president's ideal point. The respective weights are determined by the level of bureaucratic insulation. Because the second policymaking stage replicates the decision process, the bureaucracy's ideal point at the end of the second policymaking stage is a weighted average of the second president's ideal point and the bureaucracy's ideal point at the end of the first policymaking stage. Therefore the bureaucracy's ideal point at the end of the second policymaking stage is really a weighted average of three things: the bureaucracy's initial ideal point, the first president's ideal point, and the second president's ideal point. Putting weight on the first president's ideal point increases the variance of policy outcomes at the first stage, but it reduces the variance of policy outcomes in the second stage. This is the same type of benefit that the voter derives from putting weight on the bureaucracy's initial ideal point. Putting weight on the first president's ideal point, however, has lower expected costs to the voter than putting weight on the bureaucracy's initial ideal point, because the first president's ideal point is likely to be closer to the voter's ideal point in the second stage. Another way to think about this is that the bureaucracy "inherits" some of the first president's preferences, and an average of the ideal points of the first and second presidents is likely to be closer to the voter's ideal point.

Bureaucratic insulation therefore entails a tricky trade-off for the voter. Greater insulation means the first president exerts less influence over the bureaucracy, but this influence will be more lasting because it will be harder for the second president to undo. On the other hand, low bureaucratic insulation makes it easy for the first president to shift bureaucratic preferences toward her own ideal point, but it also makes it easy for the second president to shift the bureaucracy in different direction. When expected presidential responsiveness is strong relative to initial bureaucratic bias, or when voter preferences are sufficiently stable, the net effect of these considerations favors a higher level of bureaucratic insulation than in the baseline analysis.

Observe that in this case presidential deviations to the left and the fight do partially "cancel each other out," (93) but only if bureaucratic insulation is set an the appropriate intermediate level. If bureaucratic insulation is too high, then the bureaucracy's initial bias will be too "sticky" for presidents to undo. If bureaucratic insulation is too low (or if presidential influence is only temporary), then each president can effectively write on a blank slate, and policy outcomes will jump sharply to the left and fight as the presidency changes hands. With a moderate level of bureaucratic insulation and lasting presidential influence, random variations in the policy goals of different presidents will tend to cancel each other out because later presidents will partially but not completely undo the work of their predecessors.

CONCLUSION

Many legal doctrines and political institutions, as well as many proposed doctrinal and institutional reforms, are premised on the belief that increasing the influence of the entities that are most responsive to majoritarian preferences will increase the majoritarian responsiveness of policy outcomes. The dominant strain of this view argues that majoritarian values favor maximizing the president's influence over bureaucratic policymaking through a combination of broad presidential appointment and removal powers, supervisory and directive authority, agency organization, and judicial deference to agency decisions that reflect presidential priorities. On this view, appropriate limits on presidential authority to control the bureaucracy, if any, must derive from values other than democratic majoritarianism, from a rejection of the notion that the president is more responsive to national majorities than the bureaucracy or Congress, or from special considerations such as the presence of a serious credible commitment problem. The view that majoritarian values favor greater political control of the bureaucracy is not limited to strong presidentialists, however. Many who advocate greater congressional control over the bureaucracy similarly presume that bureaucratic insulation from political influence reduces the majoritarian responsiveness of bureaucratic policy outcomes.

This Article has argued that this widespread belief is flawed. The president and other elected officials may be responsive to majoritarian preferences, but they are not perfectly responsive. As a result, voters are better off if it is costly, but not impossible, for the president to influence the bureaucracy. Even though bureaucratic insulation biases the expected policy outcome away from the median voter's ideal, it also reduces the variance in outcomes relative to what would occur under absolute presidential control. Up to a point, a majority of voters benefits more from the reduction in variance than they suffer from the increase in expected policy bias. This might be thought of as an old-fashioned argument for separation of powers, (94) recast in the language of statistical decision theory: shared power over policy decisions mutes the impact of random non-majoritarian shocks to each decision maker's policy preferences.

This does not mean that strong presidentialists and others are necessarily wrong when they argue that majoritarian considerations favor greater political control of the administration than currently exists, or when they argue that such considerations militate against increases in bureaucratic autonomy. After all, if majoritarian interests are best served by an intermediate level of bureaucratic insulation, it is entirely possible that the current level of political control in some domains is either too low or just right. Nor does this Article say anything directly about which types of legal or institutional reforms are the most just or efficient means of achieving a given level of bureaucratic insulation. The analysis does, however, undermine the claim that increasing the authority of a politically responsive official, such as the president, over a politically unresponsive agency will always lead to more majoritarian policymaking. Legal or policy recommendations--for strong presidentialism or anything else--require a more nuanced assessment of the majoritarian costs and benefits of bureaucratic insulation. In particular, such recommendations must be sensitive not only to expected outcomes under different institutional arrangements but also to the variance in expected outcomes under such arrangements.

The analysis does provide some guidance as to when we should expect the optimal level of bureaucratic insulation to be high or low. Many of these predictions are straightforward. The majoritarian interest in strong presidential control is stronger when expected presidential responsiveness to majoritiarian preferences is stronger, when political parties are less polarized, when bureaucratic preferences are more distant from majoritarian preferences, and when the majority's political interests change relatively rapidly. These variables may be difficult to quantify with precision, but it may be possible to make rough qualitative estimates, as well as to assess change over time. This evidence may be useful in designing appropriate institutions in different circumstances.

The extensions considered in Section II.C suggest several additional hypotheses, some of which are less obvious. First, when presidential struggles for control of the bureaucracy impose costs on voters by distracting the president from other tasks, the optimal level of bureaucratic insulation tends to be more extreme--closer to either total agency autonomy or absolute presidential control--because aggregate control costs are lowest when the president either does not try to influence the bureaucracy or can do so at no cost.

Second, voters view bureaucratic insulation and direct political monitoring of the president as partial substitutes: both are costly means for reducing the variance of bureaucratic outcomes. Thus voters will engage in less frequent or intense direct monitoring when the bureaucracy is heavily insulated. Further, voters will prefer greater bureaucratic insulation when it is more difficult for voters to monitor a president's activities.

Third, strategic voters can offset the costs of bureaucratic insulation by selecting a "biased" president who will invest substantial effort to shift bureaucratic policy despite the costs of doing so. If voters engage in this sort of strategic behavior, the optimal level of bureaucratic insulation may be considerably higher than what one would expect if voters simply try to select a president with similar preferences.

Fourth, when bureaucratic policy issues persist over a longer period of time, optimal bureaucratic insulation tends to be lower if presidential influence is purely temporary. If each president can effect more lasting changes in bureaucratic preferences, however, optimal bureaucratic insulation may actually be higher for long-term issues than for short-term issues.

These results have application beyond the debates over strong presidentialism. For instance, they suggest a different perspective on longstanding debates over congressional preferences about agency structure and administrative process. (95) This Article suggests that electoral majorities might prefer administrative institutions that are somewhat insulated from, but somewhat responsive to, existing legislative majorities. Such institutions balance voters' interest in ensuring that their preferences influence administrative decisions on an ongoing basis (because legislative majorities will tend, on average, to reflect the preferences of current majorities) with their interest in reducing the variance of bureaucratic outcomes (which can be exacerbated by congressional control insofar as legislative preferences usually diverge somewhat from majoritarian preferences). The analysis of optimal bureaucratic insulation may also have applications outside the administrative context. For example, it may contribute to our understanding of when and to what extent courts should be insulated from the influence of the elected branches of government. (96)

The analysis in this Article is, of course, limited. It considers only a particular comparative institutional question--how much relative authority should be allocated to politically accountable politicians and politically unaccountable bureaucrats--without asking the global question of whether some other set of institutional arrangements would serve majoritarian interests even better. Also, by focusing only on an abstract case with a single politician and a single bureaucrat, the Article skirts difficult questions about the appropriate allocation of authority across a larger number of institutional actors. Moreover, the Article has deliberately bracketed vital questions about the appropriate normative objectives for institutional designers, considering instead only a simple, perhaps crude, version of majoritarianism. Despite these limitations, the analysis has shown that even under assumptions that would seem to favor maximum political control of the bureaucracy, a moderate level of bureaucratic insulation advances the interests of a majority of voters. This central finding, its underlying logic, and the implications that follow from it all suggest that many common assertions regarding the relationship between alternative institutional arrangements and important democratic values are incomplete or false.

APPENDIX

A. Players and Order of Play

Consider a simple policymaking game with three players: a representative voter (V), a president (P), and the bureaucracy (B). The game consists of two time periods indexed by t=-{0,1}, which can be thought of as the "institutional design" stage (t=0) and the "policymaking" stage (t=1).

During the institutional design stage, a bureaucracy is created to make a policy decision [x.sub.1] [member of] R. The voter's initial ideal point is [v.sub.0]=0. The bureaucracy's initial ideal point is [b.sub.0]; the absolute value of [b.sub.0] can be thought of as "initial bureaucratic bias." At the institutional design stage, the voter (or an institutional designer interested in maximizing expected voter utility) selects a level of bureaucratic insulation, [beta] [member of] [0,1]. Although [beta] is partly a function of [b.sub.0], it does not matter whether [beta] is selected before or after [b.sub.0]. If [b.sub.0] is determined before [beta], then [b.sub.0] can be interpreted as the actual level of initial bureaucratic bias. If [b.sub.0] is determined after [beta], then one can assume that initial bureaucratic bias is drawn from a known distribution with mean 0 and variance [b.sub.0.sup.2].

At the beginning of the policymaking stage (t=l), the voter's preferences may shift. Formally, the voter's period 1 ideal point is [v.sub.i]=[v.sub.0]+[[epsilon].sub.1], where [[epsilon].sub.1] is a random variable drawn from a known distribution with mean 0 and variance [[rho].sup.2]. The parameter [[rho].sup.2] can be thought of as a measure of "voter preference instability." Next, a president is chosen. The president's ideal point is [p.sub.1]=[v.sub.1]+[[alpha].sub.1], where [[alpha].sub.1] is drawn from a known distribution with mean 0 and variance [[sigma].sup.2]. The parameter [[sigma].sup.2] can be thought of as a measure of "expected presidential responsiveness," where low values of [[sigma].sup.2] indicate strong responsiveness and high values of [[sigma].sup.2] denote weak responsiveness. Absent presidential intervention, the bureaucracy's ideal point in the policymaking stage, [b.sub.1], would remain equal to [b.sub.0]. (97) The president, however, can take costly action to select a different b,. The utility cost to the president is [beta][(1-[beta]).sup.-1]-[([b.sub.1]-[b.sub.0]).sup.2]. After the president exerts her influence, the bureaucracy implements the final policy outcome, [x.sub.1], and all three players receive their final utility payoffs.

To summarize, the order of play is as follows:

Period 1 (Institutional Design Stage)

A bureaucracy is created. This bureaucracy is characterized by a level of initial bureaucratic bias ([b.sub.0]) and a level of insulation from political influence ([beta]).

Period 2 (Policymaking Stage)

Step 1: Voter preferences shift such that the voter's new ideal point is [v.sub.1]=[[epsilon].sub.1].

Step 2: The voter selects a president with ideal point [p.sub.1]= [[epsilon].sub.1]+[[alpha].sub.1].

Step 3: The president exerts costly influence over the bureaucracy, inducing a new bureaucratic ideal point [b.sub.1].

Step 4: The bureaucracy implements policy [x.sub.1] and all players receive their final utility payoffs.

B. Equilibrium Strategies

1. Equilibrium Strategy of the Bureaucracy and the President

Each player suffers a quadratic utility loss based on the distance between the final policy outcome and the player's ideal point. That is, player j's policy payoff is -[([x.sub.1]-[j.sub.1]).sup.2].

The bureaucracy, which moves last, will choose [x.sub.1.sup.*]=[b.sub.1] in equilibrium. The president chooses [b.sub.1] to maximize her expected utility, [EU.sup.P], where :

[EU.sup.P] = -[([b.sub.1] - [p.sub.1]).sup.2] - [beta] / 1 - [beta] [([b.sub.0] - [b.sub.1]).sup.2] (1)

The first term on the right-hand side of Equation (1) captures the president's expected payoff from the policy outcome (using the fact that in equilibrium the bureaucracy will choose its ideal point, [x.sub.1.sup.*] = [b.sub.1]. The second term captures the president's utility loss from the effort expended in shifting the bureaucracy's ideal point from [b.sub.0] to [b.sub.1].

It follows from Equation (1) that in equilibrium the president will induce a bureaucratic ideal point, denoted [b.sub.1.sup.*], given by:

[b.sub.1.sup.*] = (1 -[beta])[p.sub.1] + [beta][b.sub.0] = (1 - [beta])([[epsilon].sub.1] + [[alpha].sub.1])+ [beta][b.sub.0] (2)

2. Optimal Bureaucratic Insulation in the Policymaking Stage

This Article focuses primarily on the voter's optimal [beta] at the institutional design stage. Before proceeding to that issue, it is useful to consider what the voter would prefer if she could choose [beta] at the policymaking stage, after observing [v.sub.1] and [p.sub.1].

The voter's final utility, [U.sup.V], is -[([x.sub.1] - [v.sub.1]).sup.2]. Using the fact that [v.sub.1] = [[epsilon.sub.1] and that in equilibrium [x.sub.1.sup.*]=[b.sub.1.sup.*] and [b.sub.1.sup.*] is given by Equation (2), and noting that [p.sub.1]=[b.sub.1]+[[alpha].sub.1]=[[epsilon].sub.1]+[[alpha].sub.1], this utility can be rewritten as:

[U.sup.V] = -[((1 - [beta])[[alpha].sub.1] - [beta][[epsilon].sub.1] + [beta][b.sub.0]).sup.2] = -[[([v.sub.1] - [p.sub.1]) - [beta]([p.sub.1] - [b.sub.0])].sup.2] (3)

We can now calculate the voter's optimal [beta] at the policymaking stage, denoted [[beta].sup.*.sub.PM]. First, take the derivative of Equation (3) with respect to [beta], which yields:

d[U.sup.V] / d[beta] = -2[([p.sub.1] - [b.sub.0]).sup.2] ([v.sub.1] - [p.sub.1] / [p.sub.1] - [b.sub.0] + [beta]) (4)

We can assume without loss of generality that [b.sub.0][epsilon]0. If [v.sub.1]>[p.sub.1]>[b.sub.0] or [v.sub.1]<[p.sub.1]<[b.sub.0], then Equation (4) is strictly negative for all possible values of [beta], which implies [[beta].sup.*.sub.PM]=0. If [v.sub.1]>[b.sub.0]>[p.sub.1] or [v.sub.1]<[b.sub.0]<[p.sub.1], then Equation (4) is strictly positive for all possible values of [beta], which implies [[beta].sup.*.sub.PM]=1. Finally, if [b.sub.0]>[v.sub.1]>[p.sub.1] or [p.sub.1]>[v.sub.1]>[b.sub.0], the voter's optimal [beta] at the policymaking stage is:

[[beta].sub.PM.sup.*] = ([p.sub.1] - [v.sub.1] / [p.sub.1] - [b.sub.0]) [member of] (0,1) (5)

3. Optimal Bureaucratic Insulation in the Institutional Design Stage

The preceding subsection considered the voter's optimal [beta] at the policymaking stage, after [v.sub.1] and [p.sub.1], have been disclosed. In most cases, however, bureaucratic insulation is determined by institutional choices that cannot be revised easily. The remainder of the analysis therefore assumes that [beta] must be chosen at the institutional design stage. At that stage, the voter's expected utility is given by:

[EU.sup.V] = E(-[([[epsilon].sub.1] - (1 - [beta])([[epsilon].sub.1] + [[alpha].sub.1]) - [beta][b.sub.0]).sup.2]) (6)

Making use of the facts that E([[epsilon].sub.1])=E([[alpha].sub.1])=0, that the covariance of [[epsilon].sub.1] and [[alpha].sub.1] is 0, that [[sigma].sup.2]=E[([[alpha].sub.1].sup.2])-E ([alpha].sub.1]).sup.2], and that [[rho].sup.2]=E([[epsilon].sub.1.sup.2])-E([[epsilon].sub.1]).sup.2]-E [([epsilon].sub.1]).sup.2], the expression n Equation (6) simplifies to:

[EU.sup.V] = -([[beta].sup.2][[rho].sup.2] + [(1 - [beta]).sup.2][[sigma].sup.2] + [[beta].sup.2][b.sub.0.sup.2]) (7)

To solve for the voter's optimal [beta], denoted [[beta].sup.*], take the derivative of Equation (7) with respect to [beta]:

d[EU.sup.V] / d[beta] = -(2[beta][[rho].sup.2] - 2(1 - [beta])[[sigma].sup.2] + 2[beta][b.sub.0.sup.2]) (8)

By setting Equation (8) equal to 0, we can solve for [[beta].sup.*]:

[[beta].sup.*] = [[sigma].sup.2] / [[sigma].sup.2] + [[rho].sup.2] + [b.sub.0.sup.2] (9) (98)

C. Extensions

1. Social Costs of Bureaucratic Control Efforts

The basic model assumed that the effort the president expends in influencing [b.sub.1] only matters to the voter to the extent that it affects [x.sub.1]. It is possible, though, that the president's bureaucratic control struggles might affect voter utility in other ways. To capture this idea formally, assume that the voter bears some utility cost proportional to the effort the president expends on bureaucratic control. The voter's utility in this "costly effort" (CE) extension is:

[U.sup.V.sub.CE] = -[([v.sub.1] - [x.sub.1]).sup.2] - [lambda]([beta] / 1 - [beta])[([b.sub.0] - [b.sub.1]).sup.2] (10)

The second term on the right-hand side of Equation (10) is the cost to the voter of presidential bureaucratic control efforts. The [lambda]. parameter captures the significance of effort costs, relative to policy outcomes, for the voter. Notice that the basic model can be considered a special case of the costly effort extension in which [lambda]=0.

As an initial matter, it is sensible to assume that although presidential struggles with the bureaucracy entail opportunity costs for the voter, the president weighs these costs more heavily than the voter does, i.e. 1>[lambda]>0. After analyzing this case, we can examine the implications of [lambda] values outside this range.

Using Equation (10) and the equilibrium behavior of the president and bureaucracy derived earlier, the voter's expected utility can be expressed as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (11)

To find the optimal level of bureaucratic insulation under these assumptions, take the derivative of Equation (11) with respect to [beta], which yields:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (12)

Setting this expression equal to 0 and solving for [beta] yields the following expression for optimal level of bureaucratic insulation when presidential effort is costly to the voter, denoted [[beta].sub.CE.sup.*]:

[[beta].sub.CE.sup.*] = 1 / 1 - [lambda] ([[sigma].sup.2] / ([[rho].sup.2] + [[sigma].sup.2] + [b.sub.0.sup.2]) - [lambda] / 2) (13) (99)

Note that because [beta] must be in the [0,1] interval, Equation (13) will not always accurately characterize the optimal level of bureaucratic insulation. The derivative in Equation (12) is positive for all permissible values of [beta] if:

[[sigma].sup.2] / [[sigma].sup.2] + [[rho].sup.2] + [b.sub.0.sup.2] > 1 - [lambda] / 2 (14)

If this condition holds, the voter would prefer absolute bureaucratic insulation ([[beta].sub.CE.sup.*]=1). Likewise, the derivative of Equation (12) is always negative if:

[[sigma].sup.2] / [[sigma].sup.2] + [[rho].sup.2] + [b.sub.0.sup.2] < [lambda] / 2 (15)

If this condition holds, the voter would always prefer unfettered presidential control of the bureaucracy ([[beta].sub.CE.sup.*] =0).

In both of these cases, the opportunity costs to the voter of presidential control efforts are high enough that the voter would prefer to eliminate these costs altogether either by giving the president total freedom of action or by providing for absolute bureaucratic insulation. The former strategy is preferable if optimal bureaucratic insulation in the baseline case is relatively low ([[beta].sup.*]<[lambda]/2); the voter prefers the latter strategy if optimal bureaucratic insulation in the baseline case is relatively high ([[beta].sup.*]>1-[lambda]/2).

When 1-[lambda]/2>[[beta].sup.*]>[lambda]/2, we can calculate the difference between [[beta].sub.CE.sup.*] and [[beta].sup.*] by subtracting Equation (9) from Equation (13). Doing so yields:

[[DELTA].sub.CE] = [lambda]/1 -[lambda] ([[[sigma].sup.2] / ([[rho].sup.2] + [[sigma].sup.2] + [b.sub.0.sup.2]) - 1/2) (16)

Because of the assumption that 1>[lambda]>0, Equation (16) implies that when presidential control efforts entail positive opportunity costs for the voter, the voter's optimal level of bureaucratic insulation is higher than in the baseline case if [[beta].sup.*]>l/2, but lower if [[beta].sup.*]<l/2. In the special case where [[beta].sup.*]=l/2, effort costs have no effect on the optimal level of bureaucratic insulation.

The preceding discussion assumed that although presidential control efforts are costly to the voter, the voter treats these costs as less significant than does the president (i.e., 1>[lambda]>0). Although that assumption seems substantively plausible, it is worth considering how the results change when presidential effort imposes costs on the voter that are equal to or greater than the costs to the president herself ([lambda][epsilon]l), and when the voter affirmatively benefits when the president is tied down in struggles over bureaucratic policy ([lambda]<0).

When [lambda][epsilon]1, the voter prefers either absolute presidential authority or absolute bureaucratic autonomy. This follows straightforwardly from Inequalities (14) and (15): any non-zero level of presidential effort a losing proposition for the voter, because the president in equilibrium will always invest more effort in bureaucratic control than the voter would like. Therefore, the voter will simply compare her expected utility when the president has total control over the bureaucracy (-[[sigma].sup.2]) and her expected utility when the bureaucracy has complete autonomy (-([[rho].sup.2] + [b.sub.0.sup.2])).

The assumption that [lambda]>0 is based on the notion that presidential activity in areas other than bureaucratic control tends to increase expected voter utility. Under the alternative assumption that the voter affirmatively benefits from higher presidential effort costs ([lambda]<0), the optimal level of bureaucratic insulation is still given by Equation (13), and the difference between this level of insulation and the optimal level in the baseline case is still given by Equation (16). Because the sign on [lambda] is reversed, however, the substantive results are quite different. When [lambda]<0, the voter would like to induce greater presidential effort in order to distract the president from other activities. Hence, the presence of "negative opportunity costs" (or, perhaps less clumsily, "distraction benefits") makes the voter prefer a more intermediate level of bureaucratic insulation. More formally, as [lambda] decreases toward -[infinity], [[beta].sub.CE.sup.*] converges to 1/2.

A final issue to consider here is the possibility that the expected cost to the voter of presidential control efforts ([lambda]) and the expected political responsiveness of the president ([[sigma].sup.2]) might be correlated. Perhaps stronger mechanisms of political accountability in one area--bureaucratic policy--imply a greater likelihood that the policies the president's policy agenda in other areas will reflect voter preferences, which would imply that presidential control efforts impose greater opportunity costs on the voter. To explore the implications of a negative correlation between [lambda] and [[sigma].sup.2], assume that:

[lambda] = 1 / 1 + [[sigma].sup.2] (17)

The selection of this particular functional form is arbitrary, but it has the desirable feature that [lambda] is decreasing in [[sigma].sup.2] at an decreasing rate (d[lambda]/d[[sigma].sup.2]<0 [d.sup.2][lambda]/d[([[sigma].sup.2]).sup.2]>0), and the voter and the president weigh effort costs equally when the president is perfectly responsive to voter interests ([[sigma].sup.2]=0 [??] [lambda]=1). Substituting this expression for [lambda] into Equation (13) and rearranging terms yields:

[[beta].sub.CE.sup.*] = [[sigma].sup.2] + 1 / [[rho].sup.2] + [[sigma].sup.2] + [b.sub.0.sup.2] - 1 / 2[[sigma].sup.2] (18)

As before, because [beta] is bounded between 0 and 1, Equation (18) will not always characterize the optimum. We can use the same approach adopted earlier to determine [[beta].sub.CE.sup.*] when Equation (18) generates a solution outside the permissible range. First, substituting the expression for [lambda] in Equation (17) into Inequality (14) indicates that [[beta].sub.CE.sup.*] = l if:

[[sigma].sup.2] / [[rho].sup.2] + [b.sub.0.sup.2] + [[sigma].sup.2] > 1 + 2[[sigma].sup.2] / 2(1 + [[sigma].sup.2]) (19)

Similarly, substituting the expression for [lambda] in Equation (17) into Inequality (15) indicates that [[beta].sub.CE.sup.*] = 0 if:

[[sigma].sup.2] / [[rho].sup.2] + [b.sub.0.sup.2] + [[sigma].sup.2] < 1 / 2(1 + [[sigma].sup.2]) (20)

The qualitative result in this case is similar to the earlier case, except that the ranges in which the voter prefers total presidential authority or total bureaucratic autonomy are determined in part by the degree of presidential responsiveness to voter preferences. As for the case where [[beta].sub.CE.sup.*] is given by Equation (18), we can assess how the introduction of opportunity costs of presidential effort affects the voter's optimal level of bureaucratic insulation by subtracting Equation (9) from Equation (18), which yields:

[[DELTA].sub.CE] = 1 / [[rho].sup.2] + [[sigma].sup.2] + [b.sub.0.sup.2] - 1 / 2[[sigma].sup.2] = 1 / [[sigma].sup.2] ([[sigma].sup.2] / [[rho].sup.2] + [[sigma].sup.2] + [b.sub.0.sup.2] - 1 / 2) (21)

This expression makes clear that the qualitative results are the same as before: when the voter internalizes some of the president's effort costs, optimal bureaucratic insulation tends to be pushed toward the extremes. Whether opportunity costs of effort increase or decrease optimal bureaucratic insulation relative to the baseline case depends on whether [[beta].sup.*] is greater or less than 1/2. In this case, though, the degree of the difference now depends on the ratio between [[sigma].sup.2] and ([[rho].sup.2]+[b.sub.0.sup.2]). When [[sigma].sup.2] is small, introducing effort costs to the voter will have a strong effect on optimal bureaucratic insulation. But when [[sigma].sup.2] is large, the difference between optimal bureaucratic insulation in the baseline case and in the costly effort case is smaller.

2. Alternate Methods of Accountability

The baseline analysis assumed that [[sigma].sup.2] is independent of [beta]. This assumption is open to the following challenge: The expected deviation between [p.sub.1] and [v.sub.1] is due in part to how carefully the voter scrutinizes the president's actions and how aggressively the voter takes action to influence presidential preferences. If these monitoring and lobbying efforts are costly to the voter, then the voter's willingness to engage in such activities might depend on the degree to which presidential preferences actually influence bureaucratic policy outcomes. To address this issue formally, assume that at Step 1 of the policymaking stage the voter can choose to employ one of two levels of scrutiny, "low" or "high." Each level of scrutiny is associated with a different degree of presidential responsiveness, denoted [[sigma].sub.H.sup.2] and [[sigma].sub.L.sup.2], where [[sigma].sub.H.sup.2] < [[sigma].sub.L.sup.2]. Different levels of scrutiny entail different costs to the voter. The cost of low scrutiny is normalized to 0; the cost of high scrutiny is [kappa]>0. Under these assumptions (and making the arbitrary tie-breaking assumption that in the case of indifference the voter chooses low scrutiny), the voter chooses high scrutiny at Step 1 if and only if:

[(1 - [beta]).sup.2][[sigma].sub.L.sup.2] + [[beta].sup.2]([[rho].sup.2] + [b.sub.0.sup.2]) > [(1 - [beta]).sup.2] [[sigma].sub.H.sup.2] + [[beta].sup.2]([[rho].sup.2] + [b.sub.0.sup.2]) + [kappa] (22)

This condition can be re-written as:

[beta] < 1 - [square root of [kappa] / [[sigma].sub.L.sup.2] - [[sigma].sub.H.sup.2]] (23)

Inequality (23) captures the straightforward conclusion that the voter is more likely to choose high scrutiny when the monitoring and lobbying cost ([kappa]) is low, when the benefit in terms of greater presidential responsiveness ([[sigma].sub.L.sup.2] - [[sigma].sub.H.sup.2]) is high, and when the level of bureaucratic insulation ([beta]) is low. For convenience, denote the right-hand side of Inequality (23) as [tau].

To calculate the voter's optimal [beta], we must take into account the effect of different levels of insulation on the voter's monitoring and lobbying decision. Before doing so, however, it is useful to derive the voter's optimal [beta] when the subsequent level of scrutiny is taken as given. These calculations follow straightforwardly from Equation (9). If the voter is certain to choose high scrutiny in the policymaking stage, then the voter prefers:

[[beta].sub.H.sup.*] = [[sigma].sub.H.sup.2] / [[sigma].sub.H.sup.2] + [[rho].sup.2] + [b.sub.0.sup.2] (24)

Similarly, if the voter is certain to choose low scrutiny in the policymaking stage, the voter would prefer:

[[beta].sub.L.sup.*] = [[sigma].sub.L.sup.2] / [[sigma].sub.L.sup.2] + [[rho].sup.2] + [b.sub.0.sup.2] (25)

We can now calculate the optimal [beta] in the "endogenous scrutiny" (ES) extension, denoted [[beta].sub.ES.sup.*], by considering separately three cases. First, consider the case where:

[[beta].sup.*.sub.H] < [[beta].sup.*.sub.L] < [tau] (26)

In this case, [[beta].sub.ES.sup.*] = [[beta].sub.H.sup.*]. The reasoning is as follows. Because [beta] = [[beta].sub.H.sup.*] satisfies Inequality (23), the voter could rationally choose [beta]=[[beta].sub.H.sup.*] in the institutional design stage and apply high scrutiny in the policymaking stage. In contrast, because [beta]=[[beta].sub.L.sup.*] also satisfies Inequality (23), the voter cannot rationally choose [beta]=[[beta].sub.L.sup.*] in the institutional design stage and then apply low scrutiny in the policymaking stage. If [beta]=[[beta].sub.L.sup.*] under the conditions specified in Inequality (26), the voter's rational choice at the policymaking stage is high scrutiny. In order to induce low scrutiny, the voter would have to select some [beta][epsilon][tau]. Furthermore, because the voter's expected utility is decreasing in [beta] for values of [beta] above the optimum, (100) the highest expected utility the voter can achieve without inducing high scrutiny is realized when the voter chooses [beta]=[tau]. However, we know that this expected utility is lower than what the voter could achieve by setting [beta]=[[beta].sub.H.sup.*] and applying high scrutiny, because the voter is indifferent between high scrutiny and low scrutiny at [beta]=[tau], and [beta]=[[beta].sub.H.sup.*] with high scrutiny gives the voter higher expected utility than [beta]=[tau] with high scrutiny. So when Inequality (26) holds, the voter would prefer to impose lower bureaucratic insulation ([[beta].sub.H.sup.*]) at the institutional design stage and subject the president to high scrutiny at the policymaking stage.

Next, consider the case where:

[[beta].sup.*.sub.L] < [[beta].sup.*.sub.H] [greater than or equal to] [tau] (27)

In this case, [[beta].sub.ES.sup.*]=[[beta].sub.L.sup.*]. When Inequality (27) holds, the voter can rationally select [[beta].sub.L.sup.*] and low scrutiny. In contrast, the voter will not select high scrutiny when [beta]<[tau] [less than or equal to] [[beta].sub.H.sup.*]. The highest expected utility the voter can achieve with a [beta]<[tau] is still worse than the best the voter can do with [[beta].sub.L.sup.*] and low scrutiny. This follows from three facts: (1) the voter's utility under [[beta].sub.L.sup.*] with low scrutiny is greater than her utility from [beta]=[tau] with low scrutiny; (2) voter utility is increasing in [beta] for all [beta]<[tau], and (3) at [beta]=[tau], the voter is indifferent between low and high scrutiny. Thus when Inequality (27) holds, the voter would prefer greater bureaucratic insulation ([[beta].sub.L.sup.*]) coupled with lower scrutiny of the president at the policymaking stage.

The final case to consider is where:

[[beta].sup.*.sub.L] [greater than or equal to] [tau] > [[beta].sup.*.sub.H] (28)

In this case, both [[beta].sup.*.sub.L] and [[beta].sup.*.sub.H] are local maxima for the voter's expected utility function. If [beta]=[[beta].sub.H.sup.*], the voter will rationally choose high scrutiny; if [beta]=[[beta].sub.L.sup.*], the voter will rationally choose low scrutiny. Determining whether [[beta].sub.ES.sup.*] is equal to [[beta].sub.L.sup.*] or [[beta].sub.H.sup.*] requires a comparison of the voter's expected utility in each of these two cases. When Inequality (28) holds, [[beta].sub.ES.sup.*]=[[beta].sub.H.sup.*] if and only if:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (29)

Inequality (29) can be re-written as:

[[beta].sup.*2.sub.L] - [[beta].sup.*2.sub.H] > [kappa] / [[rho].sup.2] + [b.sub.0.sup.2] (30)

Therefore, if Inequalities (28) and (30) both hold, [[beta].sub.ES.sup.*]=[[beta].sub.H.sup.*]; if Inequality (28) holds but Inequality (30) does not, [[beta].sub.ES.sup.*]=[[beta].sub.L.sup.*]. All else equal, Inequality (30) is more likely to hold when monitoring and lobbying costs ([kappa]) are low and when the efficacy of scrutiny ([[sigma].sub.L.sup.2]-[[sigma].sub.H.sup.2]) is high.

3. Strategic Voter Selection of Biased Presidents

The baseline model assumed that the president's ideal point is equal to the voter's ideal point plus some random error ([p.sub.1] = [v.sub.1] + [[alpha].sub.1]). This notion of political responsiveness implies that the voter will always favor a president with an ideal point as close as possible to the voter's ideal point. This simple notion of accountability, however, is problematic. If the president must oversee a bureaucracy that does not share the voter's preferences, a strategic voter might prefer a biased president. This extension explores how the optimal [beta] differs when the voter can bias the distribution from which [p.sub.1] is drawn away from [v.sub.1]. In particular, assume that [p.sub.1]=[v.sub.1] + [mu] + [[alpha].sub.1], where [mu] is the level of "presidential bias," selected strategically by the voter prior to Step 2 of the policymaking stage. That is, the voter selects [mu] after observing [b.sub.0] and [beta], but before learning [[alpha].sub.1]. For simplicity, assume that the selection of [mu] does not impose any direct costs on the voter.

Working backwards, we first calculate the bureaucratic ideal point the president will induce at Step 3 of the policymaking stage by taking the derivative of Equation (1) with respect to [b.sub.1], substituting in [p.sub.1]=[[epsilon].sub.1] + [mu] + [[alpha].sub.1], and setting the resulting expression equal to 0. Doing so yields the bureaucracy's equilibrium ideal point in the "strategic voting" (SV) extension, [b.sub.SV.sup.*]:

[b.sub.SV.sup.*] = (1 - [beta])([[epsilon].sub.1] + [mu] + [[alpha].sub.1]) + [beta][b.sub.0] (31)

We can substitute this expression into Equation (3) to derive the following expression for the voter's utility:

[U.sup.V.sub.SV] = [((1 - [beta])[[alpha].sub.1] + (1 - [beta])[mu] - [beta][[epsilon].sub.1] + [beta][b.sub.0]).sup.2] (32)

The expected utility for the voter at the beginning of the policymaking stage (the moment when the voter must select [mu]) is therefore:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (33)

By taking the derivative with of Equation (33) with respect to [mu], we can calculate the level of presidential bias a rational voter would select in equilibrium, denoted [[mu].sup.*]:

[[mu].sup.*] = -([beta] / 1 - [beta])([b.sub.0] - [[epsilon].sub.1]) (34)

Notice two features of [[mu].sup.*]. First, it is proportional to, but has the opposite sign as, the sum of the bureaucracy's initial bias ([b.sub.0]) and the voter's period 1 ideal point ([[epsilon].sub.1]). In other words, a strategic voter prefers a president whose bias goes in the opposite direction as the bureaucracy's bias at the beginning of period 1 (after the voter's preferences have shifted). Second, [[mu].sup.*] is increasing in [beta]. The more the bureaucracy is shielded from presidential control, the more the voter prefers a president whose ideal point deviates from the voter's.

We derive the voter's utility, when she induces her optimal level of presidential bias, by substituting the expression for [[mu].sup.*] from Equation (34) into Equation (32), which yields:

[U.sup.V.sub.SV] = -[((1 - [beta])[[alpha].sub.1]).sup.2] (35)

Thus the voter's expected utility at the institutional design stage is:

[EU.sup.V.sub.ID-SV] = -[(1 - [beta]).sup.2][[sigma].sup.2] (36)

Equation (36) implies that when the voter can strategically bias the president without bearing additional costs for doing so, the voter prefers that the bureaucracy be almost completely free from presidential control (i.e., [[beta].sub.SV.sup.*] is infinitesimally below 1). The reason is that the voter can offset the costs associated with bureaucratic insulation simply by increasing the bias of the president in the opposite direction. Thus the voter's only interest is in reducing the impact of [[sigma].sup.2] on the final outcome. As [beta] approaches 1, the variance of the policy outcome goes to 0 (although if [beta]=1 then the president cannot influence the bureaucracy at all, and the voter would not be able to offset bureaucratic bias).

4. Longer Time Horizons

The baseline model included a single policymaking stage. This extension considers how the results change in a multi-period model with three periods indexed by t={0,1,2}. As before, period t=0 is the institutional design stage and period t=1 is a policymaking stage. Period t=2 is a second policymaking stage. At the beginning of period 2, voter preferences may shift again: the voter's period 2 ideal point is [v.sub.2]=[v.sub.1]+[[epsilon].sub.2], where [[epsilon].sub.2] is an independent draw from a distribution with mean 0 and variance [[rho].sup.2]. The period 2 president's ideal point is [p.sub.2]=[v.sub.2]+ [[alpha].sub.2], where [[alpha].sub.2] is independently drawn from a distribution with mean 0 and variance [[sigma].sup.2]. The president then selects a new bureaucratic ideal point, [b.sub.2], and the bureaucracy selects a new policy, [x.sub.2]. The president in each period is treated as a separate player that cares only about her utility payoff in that period; the same is true of the bureaucracy. (101) The voter's utility is the sum of her payoffs in periods 1 and 2.

In order to compare the voter's optimal [beta] in this extension to the baseline model, we must make some further assumptions regarding whether the modifications in the bureaucracy's ideal point induced by the period 1 president "stick" in period 2. One possibility is that a president's influence on bureaucratic preferences lasts only as long as that president is in office; once the president departs, the bureaucracy's ideal point reverts to its initial value, [b.sub.0], until the new president exerts her influence. An alternative possibility is that each president's influence on the bureaucracy lasts until future presidential action. On this view, the bureaucracy's default ideal point in period 2 is [b.sub.1] rather than [b.sub.0]. The analysis will consider each of these possibilities.

In the "temporary influence" (TI) case, where each president's influence over bureaucratic policy preferences lasts only as long as that president is in office, the president in equilibrium will induce the following period 2 bureaucratic ideal point:

[b.sup.*.sub.2-TI] = -(1 - [beta])[p.sub.2] + [beta]b.sub.0] (37)

This means that the voter's utility in the second policymaking stage is:

[U.sup.V.sub.2-TI] = -[((1 - [beta])([[epsilon].sub.1] + [[epsilon].sub.2] + [[alpha].sub.2]) + [beta][b.sub.0] - ([[epsilon].sub.1] + [[epsilon].sub.2])).sup.2] (38)

At the institutional design stage, then, the voter's expected period 2 utility is:

[EU.sup.V.sub.2-TI] = -[(1 - [beta]).sup.2][[sigma].sup.2] - [[beta].sup.2] ([b.sub.0.sup.2] + 2[[rho].sup.2]) (39)

The voter's total expected utility in the "temporary influence" version of the three-period model is simply the sum of Equations (7) and (39). We can calculate the optimal [beta] by taking the derivative of this sum with respect to [beta]. Doing so yields:

[[beta].sup.*.sub.TI] = [[sigma].sup.2] / [[sigma].sup.2] + [b.sub.0.sup.2] + 3/2 [[rho].sup.2] (40)

Except in the special case where [rho]=0, the optimal [beta] is lower in the multi-period model with temporary presidential influence than in the basic model (i.e. [[beta].sub.TI.sup.*]<[[beta].sub.ID.sup.*]).

In the case where each president has a "lasting influence" (LI) over bureaucratic policy preferences, the period 2 president will induce the following bureaucratic ideal point in equilibrium:

[b.sup.*.sub.2-LI] = (1 - [beta])[p.sub.2] + [beta][b.sub.1] = (1 - [beta])[p.sub.2] + [beta]((1 - [beta])[p.sub.1] + [beta][b.sub.0]) (41)

Thus the voter's utility in the second policymaking stage is:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (42)

At the institutional design stage, then, the voter's expected period 2 utility is:

[EU.sup.V.sub.2-LI] = (1 + [[beta].sup.2])[(1 - [beta]).sup.2][[sigma].sup.2] + [[beta].sup.2](1 + [[beta].sup.2])[[rho].sup.2] + [[beta].sup.4][b.sub.0.sup.2] (43)

Rather than solving directly for the optimal [beta] (denoted [[beta].sub.LI.sup.*]), we can verify the existence of a unique [[beta].sub.LI.sup.*] between 0 and 1, and then evaluate whether it is greater or less than [[beta].sup.*]. First, taking the derivative of the expected value of the multi-period game (the sum of Equations (7) and (43)) with respect to [beta] yields:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (44)

Evaluating this expression at [beta]=0 yields 4[[sigma].sup.2]>0, while evaluating the expression at [beta]=1 yields -(8[[rho].sup.2] + 6[b.sub.0.sup.2]) < 0. Next, the second derivative of the voter's expected value respect to [beta] yields:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (45)

From these two facts it follows that there a unique [[beta].sub.LI.sup.*] between 0 and 1 that maximizes the voter's expected utility in the lasting influence case. All that remains is to determine whether this [[beta].sub.LI.sup.*] is greater or less than [[beta].sup.*]. To do this, we can evaluate Equation (44) at [[beta]=[[beta].sup.*]. A positive value implies [[beta].sub.LI.sup.*]>[[beta].sup.*]. To see why, note first that [[beta].sub.LI.sup.*] is the value of [beta] for which Equation (45) is equal to 0. Because Equation (45) establishes that this derivative is decreasing in [beta], if Equation (44) is positive at [beta]=[[beta].sup.*], it must be equal to 0 at some [[beta]>[[beta].sub.ID.sup.*]. By similar logic, if Equation (44) is negative at [[beta]=[[beta].sup.*], then it must be that [[beta].sub.LI.sup.*]<[[beta].sub.ID.sup.*]. If Equation (45) is equal to 0 at [beta]=[beta].sup.*], then [[beta].sub.LI.sup.*] = [[beta].sub.ID.sup.*]. Evaluating Equation (44) at [beta]=[[beta].sup.*] yields:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (46)

This sign of this expression depends on the sign of:

[gamma] [equivalent to] ([[sigma].sup.2] - [b.sub.0.sup.2])[[rho].sup.2] - [b.sub.0.sup.4] (47)

If [gamma] [less than or equal to] 0, Equation (46) is weakly positive, implying [[beta].sub.LI.sup.*] [epsilon][[beta].sup.*]. This holds true if (1) [[sigma].sup.2] [less than or equal to] [b.sub.0.sup.2]; or (2) [[sigma].sup.2] > [b.sub.0.sup.2] and [[rho].sup.2] [less than or equal to] ([b.sub.0.sup.4] / ([[sigma].sup.2] - [b.sub.0.sup.2]). If [gamma] > 0, Equation (45) is negative, implying [[beta].sub.LI.sup.*] < [[beta].sup.*]. This holds true if [[sigma].sup.2] > [b.sub.0.sup.2] [[rho].sup.2] > ([b.sub.0.sup.4] / ([[sigma].sup.2] - [b.sub.0.sup.2]). Substantively, these results indicate that if the president has a lasting influence over bureaucratic preferences, adding additional policymaking periods strengthens the interest in bureaucratic insulation if presidential responsiveness is strong ([[sigma].sub.2]; low), initial bureaucratic drift is relatively large ([b.sub.0.sup.2] high), and voter preferences are relatively stable ([[rho].sup.2] low). In contrast, the voter's interest in bureaucratic insulation is weaker in the multi-period model if presidential responsiveness is weak ([[sigma].sup.2] high), initial bureaucratic drift is not too severe ([b.sub.0.sup.2] low), and voter preferences are unstable ([[rho].sup.2] high).

(1.) Lloyd N. Cutler & David R. Johnson, Regulation and the Political Process, 84 YALE L.J. 1395, 1399 (1975).

(2.) Id.

(3.) This challenge is based on social choice theory findings that, at least for multidimensional issues, it is impossible to aggregate individual preferences into coherent social preferences without sacrificing either democratic decision making or weak rationality criteria. See KENNETH J. ARROW, SOCIAL CHOICE AND INDIVIDUAL VALUES (1951); cf. Richard McKelvey, Intransitivities in Multidimensional Voting Models and Some Implications for Agenda Control, 12 J. ECON. THEORY 472 (1976) (showing that, for multidimensional issues, sophisticated agenda setters can manipulate the order of majority votes to get any outcome, no matter the distribution of voter preferences). Some believe these findings imply that one cannot speak coherently of the "intent" or "preference" of a collective body such as an electorate or legislature. See WILLIAM H. RIKER, LIBERALISM AGAINST POPULISM (1982); Kenneth A. Shepsle, Congress is a "They," Not an "It": Legislative Intent as Oxymoron, 12 INT'L REV. L. & ECON. 239 (1992). Others, however, reject the conclusion that these social-choice results undermine the normative coherence of majoritarianism. See GERRY MACKIE, DEMOCRACY DEFENDED (2003); Richard H. Pildes & Elizabeth S. Anderson, Slinging Arrows at Democracy: Social Choice Theory; Value Pluralism, and Democratic Politics, 90 COLUM. L. REV. 2121 (1990). And others have argued that, whatever the theoretical problems with multidimensional democratic choice, most real-world political issues appear to be one-dimensional, with a stable majority and a stable minority on each side, and that on these issues it is meaningful to speak of what the majority prefers. See KEITH Z. POOLE & HOWARD ROSENTHAL, CONGRESS: A POLITICAL-ECONOMIC HISTORY OF ROLL CALL VOTING (1997); John Mark Hansen, Individuals, Institutions, and Public Preferences over Public Finance, 92 AM. POE. SCI. REV. 513 (1998).

(4.) This may occur if the marginal cost to the median voter of supplying a public good differs from the total marginal social cost. See JOSEPH E. STIGLITZ, ECONOMICS OF THE PUBLIC SECTOR 137-41 (3d ed. 2000). Another hypothesis is that political competition in a majoritarian system leads to inefficient redistribution, retarding long-term growth. See Samuel E Huntington & Jorge I. Dominguez, Political Development, in 3 HANDBOOK OF POLITICAL SCIENCE 60 (Fred I. Greenstein & Nelson W. Polsby eds., 1975). Additionally, some have argued that systematic cognitive biases lead a majority of voters to demand inefficient policies. See BRYAN CAPLAN, THE MYTH OF THE RATIONAL VOTER (2007).

(5.) Possible normative constraints on majoritarian decision making include protecting the interests of those who are not represented, or cannot adequately protect their interests, in the political process, see JOHN HART ELY, DEMOCRACY AND DISTRUST (1980), and advancing a conception of the public good that incorporates more than the welfare of individual voters, see RONALD DWORKIN, FREEDOM'S LAW (1996).

(6.) Richard J. Pierce, Jr., The Role of Constitutional and Political Theory in Administrative Law, 64 TEX. L. REV. 469, 520 (1985).

(7.) Peter L. Strauss & Cass R. Sunstein, The Role of the President and OMB in Informal Rulemaking, 38 ADMIN. L. REV. 181, 183 (1986).

(8.) See Jeffrey S. Banks & Barry R. Weingast, The Political Control of Bureaucracies under Asymmetric Information, 36 AM. J. POE. SCI. 509 (1992); David B. Spence, Agency Policy Making and Political Control: Modeling Away the Delegation Problem, 7 J. PUB. ADMIN. RES. & THEORY 199 (1997).

(9.) See Philippe Aghion & Jean Tirole, Formal and Real Authority in Organizations, 105 J. POL. ECON. 1 (1997); Jonathan Bendor & Adam Meirowitz, Spatial Models of Delegation, 98 AM. POL. SCI. REV. 293 (2004); Sean Gailmard & John W. Patty, Slackers and Zealots: Civil Service, Policy Discretion and Bureaucratic Expertise, 51 AM. J. POL. SCI. 873 (2007); cf. Neal Kumar Katyal, Internal Separation of Powers: Checking Today's Most Dangerous Branch from Within, 115 YALE L.J. 2314, 2324-27 (2006) (arguing that excessive presidential control of agencies can reduce the flow of valuable information from agencies to the president).

(10.) See Witold Jerzy Henisz, Political Institutions and Policy Volatility, 16 ECON. & POL. 1 (2004); Finn E. Kydland & Edward C. Prescott, Rules Rather Than Discretion: The Inconsistency of Optimal Plans, 85 J. POL. ECON. 473 (1977); Brian Levy & Pablo T. Spiller, The Institutional Foundations of Regulatory Commitment: A Comparative Analysis of Telecommunications Regulation, 10 J.L. ECON. & ORG. 201 (1994).

(11.) See Matthew C. Stephenson, Legislative Allocation of Delegated Power: Uncertainty, Risk, and the Choice Between Agencies and Courts, 119 HARV. L. REV. 1036 (2006).

(12.) See ELY, supra note 5; Samuel Issacharoff, Gerrymandering and Political Cartels, 116 HARV. L. REV. 593, 643-48 (2002); Richard H. Pildes, The Supreme Court, 2003 Term, Foreword: The Constitutionalization of Democratic Politics, 118 HARV. L. REV. 28 (2004).

(13.) See THEODORE J. LOWI, THE END OF LIBERALISM (1969); DAVID SCHOENBROD, POWER WITHOUT RESPONSIBILITY (1993); Peter H. Aranson et al., A Theory of Legislative Delegation, 68 CORNELL L. REV. 1 (1982); Scott Baker & Kimberly D. Krawiec, The Penalty Default Canon, 72 GEO. WASH. L. REV. 663 (2004); cf. Indus. Union Dep't v. Am. Petroleum Inst., 448 U.S. 607, 685-88 (1980) (Rehnquist, J., concurring); Am. Trucking Ass'ns v. EPA, 175 F.3d 1027, 1034-40 (D.C. Cir. 1999), rev 'd sub nom. Whitman v. Am. Trucking Ass'ns, 531 U.S. 457 (2001).

(14.) See David Epstein & Sharyn O'Halloran, The Nondelegation Doctrine and the Separation of Powers: A Political Science Approach, 20 CARDOZO L. REV. 947 (1999); Jerry L. Mashaw, Prodelegation." Why Administrators Should Make Political Decisions, 1 J.L. ECON. & ORG. 81 (1985); Eric A. Posner & Adrian Vermeule, Interring the Nondelegation Doctrine, 69 U. CHI. L. REV. 1721 (2002); Peter H. Schuck, Delegation and Democracy: Comments on David Schoenbrod, 20 CARDOZO L. REV. 775 (1999); Mark Seidenfeld, Pyrrhic Political Penalties: Why the Public Would Lose Under the "Penalty Default Canon ", 72 GEO. WASH. L. REV. 724 (2004).

(15.) See Whitman, 531 U.S. 457; Mistretta v. United States, 488 U.S. 361 (1989).

(16.) See John E Manning, The Nondelegation Doctrine as a Canon of Avoidance, 2000 SUP. CT. REV. 223; Cass R. Sunstein, Nondelegation Canons, 67 U. CHI. L. REV. 315 (2000); Gonzales v. Oregon, 546 U.S. 243 (2006); FDA v. Brown & Williamson Tobacco Corp., 529 U.S. 120 (2000); Am. Petroleum Inst., 448 U.S. 607 (plurality opinion).

(17.) See Lisa Schultz Bressman, Procedures as Politics in Administrative Law, 107 COLUM. L. REV. 1749 (2007); cf. EINER ELHAUGE, STATUTORY DEFAULT RULES (2008) (arguing that courts can and should use interpretive default rules that implement the policies that are most likely to be enactable by the current president and Congress, if courts can reliably infer these policies from official action).

(18.) Lawrence Lessig & Cass R. Sunstein, The President and the Administration, 94 COLUM. L. REV. 1, 103 (1994); see also Cass R. Sunstein, Changing Conceptions of Administration, 1987 BYU L. REV. 927, 938 (1987). Lessig and Sunstein argue that the Framers did not believe the Constitution required a unitary executive, but that this is because they failed to anticipate the inescapably political nature of bureaucratic decision making in the modern administrative state. Lessig & Sunstein, supra, at 102-03.

(19.) E.g., James F. Blumstein, Regulatory Review by the Executive Office of the President: An Overview and Policy Analysis of Current Issues, 51 DUKE LJ. 851, 885 (2001) ("An administration whose policies and goals may be out of sync with the culture or values of an agency ... is well advised to improve the oversight role of its political appointees.... It is fair for this point to travel under the label of improved political accountability."); id. at 887 ("Given that agency rulemaking does contemplate a role for political input ... it becomes hard to see why a presidential administration should not direct or at least influence its agents' exercise of discretion within the agency bureaucracy.").

(20.) E.g., Steven G. Calabresi, Some Normative Arguments for the Unitary Executive, 48 ARK. L. REV. 23, 67 (1995). Calabresi states:
   The President of the United States and his subordinates are the
   conscious agents of ... a national majority coalition. If that
   coalition will, by its very nature, be likely to be moderate,
   temperate, and just, so too will its agent be likely to be
   moderate, temperate, and just.... [M]ost presidents ... will work
   every day they are in office to try to keep their policies in
   accord with the wise and benevolent preferences of the national
   majority....


Id.

(21.) E.g., Philip J. Harter, Executive Oversight of Rulemaking: The President Is No Stranger, 36 AM. U. L. REV. 557, 568 (1987) ("We vote for presidents, not secretaries or administrators.... White House oversight places accountability precisely where it should be, namely, where the electorate can do something about it."). He continues:
   Presidential oversight.... broadens what may be an unduly parochial
   approach by an agency and helps the agency take other values into
   account when reaching important decisions.... Presidential
   oversight is a means of incorporating the prevailing political
   climate into an agency's discretion while maintaining allegiance to
   the relevant factors defined in the legislation.


Id. at 570-71.

(22.) E.g., Elena Kagan, Presidential Administration, 114 HARV. L. REV. 2245, 2384 (2001) ("Presidential administration ... advances political accountability by subjecting the bureaucracy to the control mechanism most open to public examination and most responsive to public opinion.").

(23.) E.g., Mashaw, supra note 14, at 95-96. He states:
   [T]he utilization of vague delegations to administrative agencies
   ... [is] a device for facilitating responsiveness to voter
   preferences expressed in presidential elections.... [O]ne can
   reasonably expect that a president will be able to affect policy in
   a four-year term only because being elected president entails
   acquiring the power to exercise, direct, or influence policy
   discretion.


Id.; accord JERRY L. MASHAW, GREED, CHAOS, & GOVERNANCE 152-53 (1997).

(24.) E.g., Pierce, supra note 6, at 508 ("Presidents are elected presumably because they share the policy preferences of a majority of citizens. It follows that they should be permitted to determine social policy within whatever boundaries Congress has established."); Richard J. Pierce, Jr., The Role of the Judiciary in Implementing an Agency Theory of Government, 64 N.Y.U.L. REV. 1239 (1989) [hereinafter Pierce, Agency Theory].

(25.) E.g., Strauss & Sunstein, supra note 7, at 190 (1986). Strauss and Sunstein write:
   [T]he President ... [is] uniquely well-situated to design
   regulatory policy in a way that is responsive to the interests of
   the public as a whole. Agency officials, by contrast, are only
   indirectly accountable.... For these reasons, a supervisory role by
   the President should help ensure that discretionary decisions by
   regulatory agencies are responsive to the public generally.


Id. Strauss, however, has criticized strong presidentialism on other grounds. See Peter L. Strauss, The Place of Agencies in Government: Separation of Powers and the Fourth Branch, 84 COLUM. L. REV. 573 (1984); Peter L. Strauss, Presidential Rulemaking, 72 CHI.-KENT L. REV. 965 (1997).

(26.) See, e.g., Steven G. Calabresi & Saikrishna B. Prakash, The President's Power To Execute the Laws, 104 YALE L.J. 541 (1994); Calabresi, supra note 20.

(27.) Kagan, supra note 22, at 2336.

(28.) Id.

(29.) Id. at 2337.

(30.) Id. at 2334 (emphasis added).

(31.) Strauss & Sunstein, supra note 7, at 183.

(32.) See id. at 190.

(33.) This formulation is question-begging insofar as it does not define "competence" or "fairness" precisely or indicate how much erosion of these values would count as "excessive." Clarifying these issues, however, is not necessary to establish the basic point at hand: the strong presidentialists assume that, all else equal, the marginal benefit of increased presidential control is generally positive, and even if there are countervailing concerns, a relatively high degree of presidential control is good unless and until these countervailing costs become sufficiently large.

(34.) See, e.g., FDA v. Brown & Williamson Tobacco Corp., 529 U.S. 129, 190 (2000) (Breyer, J., dissenting) ("Insofar as the decision to regulate tobacco reflects the policy of an administration, it is a decision for which that administration, and those politically elected officials who support it, must (and will) take responsibility."); Chevron U.S.A. v. Natural Res. Def. Council, 467 U.S. 837, 865 (1984). The Court held in Chevron:
   [A]n agency to which Congress has delegated policymaking
   responsibilities may, within the limits of that delegation,
   properly rely upon the incumbent administration's views of wise
   policy to inform its judgments. While agencies are not directly
   accountable to the people, the Chief Executive is, and it is
   entirely appropriate for this political branch of the Government to
   make such policy choices....


Id. For further discussion on this point, see Thomas W. Merrill, Judicial Deference to Executive Precedent, 101 YALE L.J. 969, 978-80 (1992); Pierce, supra note 6, at 520-24; Pierce, Agency Theory, supra note 24, at 1255-58; Cass R. Sunstein & Adrian Vermeule, Interpretation and Institutions, 101 MICH. L. REV. 885, 925-28 (2003).

(35.) See CHRISTOPHER F. EDLEY, JR., ADMINISTRATIVE LAW: RETHINKING JUDICIAL CONTROL OF THE BUREAUCRACY 33-34, 6245, 181-84 (1990); Pierce, Agency Theory, supra note 24, at 1259-60, 1263-67.

(36.) See David J. Barron & Elena Kagan, Chevron's Nondelegation Doctrine, 2001 SUP. CT. REV. 201; Kagan, supra note 22, at 2372-82.

(37.) See Rust v. Sullivan, 500 U.S. 173, 186-87 (1991); Motor Vehicles Mfrs. Ass'n v. State Farm Mut. Auto. Ins. Co., 463 U.S. 29, 59 (1983) (Rehnquist, J., dissenting); Matthew C. Stephenson, Public Regulation of Private Enforcement: The Case for Expanding the Role of Administrative Agencies, 91 VA. L. REV. 93, 139-42 (2005).

(38.) See Exec. Order No. 12,866, 3 C.F.R. 638 (1993); Exec. Order No. 12498, 3 C.F.R. 323 (1985); Exec. Order No. 12,291, 46 Fed. Reg. 13,193 (Feb. 17, 1981); Blumstein, supra note 19; Christopher C. DeMuth & Douglas H. Ginsburg, Commentary, White House Review of Agency Rulemaking, 99 HARV. L. REV. 1075 (1986); John O. McGinnis, Presidential Review as Constitutional Restoration, 51 DUKE L.J. 901 (2001); Strauss & Sunstein, supra note 7, at 190.

(39.) See Cutler & Johnson, supra note 1; Kagan, supra note 22, at 2290-99, 2331-45.

(40.) See Michael Herz, Imposing Unified Executive Branch Statutory Interpretation, 15 CARDOZO L. REV. 219 (1993).

(41.) See Exec. Order No. 13,422, 72 Fed. Reg. 2763 (Jan. 23, 2007) (amending Executive Order 12,866 to require each agency to designate a presidential appointee as the agency's "Regulatory Policy Officer" to supervise agency regulatory plans and ensure compliance with OMB supervision); Blumstein, supra note 19.

(42.) See Calabresi, supra note 20, at 82-86; Lessig & Sunstein, supra note 18, at 106-08, 110-14; Geoffrey E Miller, Independent Agencies, 1986 SUP. CT. REV. 41.

(43.) See supra note 5.

(44.) Lisa Schultz Bressman, Beyond Accountability: Arbitrariness and Legitimacy in the Administrative State, 78 N.Y.U.L. REV. 461 (2003); see also KENNETH CULP DAVIS, DISCRETIONARY JUSTICE (1969); Louis L. JAFFE, JUDICIAL CONTROL OF ADMINISTRATIVE ACTION (1965).

(45.) See Cynthia R. Farina, The Consent of the Governed: Against Simple Rules for a Complex World, 72 CHI.-KENT L. REV. 987, 988, 1004-07 (1997); Martin S. Flaherty, The Most Dangerous Branch, 105 YALE L.J. 1725, 1824-25 (1996).

(46.) See SCHOENBROD, supra note 13, at 105-06; Flaherty, supra note 45, at 1824-25; Jide Nzelibe, The Fable of the Nationalist President and the Parochial Congress, 53 UCLA L. REV. 1217 (2006); Thomas O. Sargentich, The Emphasis on the Presidency in U.S. Public Law: An Essay Critiquing Presidential Administration, 59 ADMIN. L. REV. l, 29-32 (2007); Peter M. Shane, Political Accountability in a System of Checks and Balances: The Case of Presidential Review of Rulemaking, 48 ARK. L. REV. 161, 200 (1995); cf. William N. Eskridge, Jr. & John Ferejohn, Making the Deal Stick: Enforcing the Original Constitutional Structure of Lawmaking in the Modern Regulatory State, 8 J.L. ECON. & ORG. 165 (1992) (arguing that separation of powers law should shift influence from the president to Congress in order to preserve the original constitutional design).

(47.) See Lisa Schultz Bressman & Michael P. Vandenbergh, Inside the Administrative State: A Critical Look at the Practice of Presidential Control, 105 MICH. L. REV. 47, 84 (2006); Bressman, supra note 17; Steven P. Croley, Theories of Regulation: Incorporating the Administrative Process, 98 COLUM. L. REV. 1, 59-60 (1998); Katyal, supra note 9, at 2344-45; Richard B. Stewart, The Reformation of American Administrative Law, 88 HARV. L. REV. 1667, 1712 (1975). This view is related to the claim that the administrative process can foster "civic republicanism." See Mark Seidenfeld, A Civic Republican Justification for the Bureaucratic State, 105 HARV. L. REV. 1511 (1992). The main difference is that civic republicans do not view the purpose of the political or bureaucratic process simply as aggregating preexisting preferences; rather, they emphasize the role of rational deliberation in shaping individual preferences and realizing some collective conception of the public good. See id. at 1514.

(48.) See Bressman & Vandenbergh, supra note 47, at 78-84; Katyal, supra note 9, at 2343-44; Thomas O. McGarity, Presidential Control of Regulatory Agency Decisionmaking, 36 AM. U. L. REV. 443, 451, 456-57 (1987); Alan B. Morrison, Commentary, OMB Interference with Agency Rulemaking: The Wrong Way To Write a Regulation, 99 HARV. L. REV. 1059, 1064, 1067-68 (1986); Robert V. Percival, Presidential Management of the Administrative State: The Not-So-Unitary Executive, 51 DUKE L.J. 963, 1009-10 (2001).

(49.) See Farina, supra note 45, at 988, 992-1007; Edward Rubin, The Myth of Accountability and the Anti-administrative Impulse, 103 MICH. L. REV. 2073, 2073 (2005); Shane, supra note 46, at 196.

(50.) But see Rubin, supra note 49, at 2078.

(51.) In the formal model presented in Section B of the Appendix, the voter's ideal point is [v.sub.1], the policy ultimately implemented is [x.sub.1], and the voter's utility is -[([x.sub.1]-[v.sub.1]).sup.2]. Expected policy responsiveness is E(-[([x.sub.1]-[v.sub.1]).sup.2]. See infra Section B.I of the Appendix.

(52.) Likewise, the analysis would be qualitatively the same if the politically responsive official were labeled "president" and the unresponsive entity were labeled "Congress," or vice versa. The basic framework can apply in any situation in which two actors potentially share responsibility for a policy outcome, and one of those two actors is more responsive to voter preferences than the other.

(53.) In the formal analysis, the two stages are denoted by t={0,1}, where t=-0 is the institutional design stage and t=1 is the policymaking stage. See infra Section A of the Appendix.

(54.) In the formal model, the voter's initial ideal point, [v.sub.0], is normalized to zero, and initial bureaucratic bias is denoted [b.sub.0]. See infra Section A of the Appendix.

(55.) In the formal analysis, the level of bureaucratic insulation is given by [beta]. See infra Section A of the Appendix. While the text implies that the bureaucracy's initial bias is known when the level of bureaucratic insulation is chosen, this assumption is not necessary for the analysis. One could assume instead that the bureaucracy's initial ideal point is realized after the level of bureaucratic insulation has been selected. In that case, "initial bureaucratic bias" should be reinterpreted as the expected distance (or, more accurately, the expected square of the distance) between the bureaucracy's initial ideal point and the voter's initial ideal point.

(56.) Formally, the voter's ideal point in the policymaking stage is [v.sub.t]=[v.sub.0]+[[epsilon].sub.1], where [[epsilon].sub.1], is a random draw from a known distribution with mean 0 and variance [[rho].sup.2]. "Voter preference instability" is simply the variance, [[rho].sup.2]. See infra Section A of the Appendix.

(57.) See Calabresi, supra note 20, at 68-69.

(58.) In the formal analysis, the president's ideal point is [p.sub.1]=[v.sub.1]+[[alpha].sub.1], where [[alpha].sub.1], is a random variable drawn from a known distribution with mean 0 and variance [[sigma].sup.2]. See infra Section A of the Appendix.

(59.) Compare Mashaw, supra note 14, at 95 (arguing that citizens select presidents on the basis of the candidates' perceived policy agendas), with Kagan, supra note 22, at 2334-35 (asserting that the threat of voter punishment keeps presidential policy roughly in line with majoritarian preferences). For a general discussion contrasting these accountability mechanisms, see James D. Fearon, Electoral Accountability and the Control of Politicians: Selecting Good Types versus Sanctioning Poor Performance, in DEMOCRACY, ACCOUNTABILITY, AND REPRESENTATION 55 (Adam Przeworski et al. eds., 1999).

(60.) See Calabresi, supra note 20, at 69-70 & n.114; Kagan, supra note 22, at 2334-37.

(61.) Calabresi, supra note 20, at 69.

(62.) Id. at 70n.114.

(63.) Formally, expected presidential responsiveness is measured by the variance [[sigma].sup.2], where lower values of [[sigma].sup.2] correspond to higher levels of expected presidential responsiveness. See infra Section A of the Appendix.

(64.) See ANTHONY DOWNS, INSIDE BUREAUCRACY 158-64 (1967); Louis L. Jaffe, The Effective Limits of the Administrative Process: A Reevaluation. 67 HARV. L. REV. 1105, 1109 (1954); Kagan, supra note 22, at 2336-37.

(65.) Section A of the Appendix establishes this point formally. See infra note 97.

(66.) In the formal analysis, the president can shift the bureaucracy's ideal point from [b.sub.0] to [b.sub.1] at utility cost ([beta]/(1-[beta]))[([b.sub.0]-[b.sub.1]).sup.2]. See infra Section A of the Appendix. Section B.1 of the Appendix provides a more complete analysis of the president's equilibrium behavior. This modeling approach contrasts with other approaches taken in the social science literature. First, much of the formal literature on bureaucracy and separation of powers assumes that the principal (such as a voter or legislator) faces a dichotomous choice between assigning authority to one institution and assigning it to another. See Alberto Alesina & Guido Tabellini, Bureaucrats or Politicians? Part I: A Single Policy Task, 97 AM. ECON. REV. 169 (2007); Eric Maskin & Jean Tirole, The Politician and the Judge: Accountability in Government, 94 AM. ECON. REV. 1034 (2004); Stephenson, supra note 11. Second, much of the literature assumes either that the principal can revise or reject its agent's proposal costlessly or that the principal bears a fixed cost for altering the agent's decision. See Pablo T. Spiller, Agency Discretion Under Judicial Review, 16 MATHEMATICAL COMPUTER MODELLING 185, 193-95 (1992); Emerson H. Tiller & Pablo T. Spiller, Strategic Instruments: Legal Structure and Political Games in Administrative Law, 15 J.L. ECON. &. ORG. 349, 354-56 (1999). In contrast, this Article assumes that the president and the bureaucracy share joint responsibility for the policy outcome, and that the president's control cost is an increasing function of how much the president changes the final outcome from what the bureaucracy initially preferred. For a similar modeling approach in a different but related substantive context, see Alan E. Wiseman, Delegation and Positive-Sum Bureaucracies (AEI-Brookings Joint Ctr. for Reg. Stud., Working Paper No. 07-05), available at http://papers.ssrn.com/sol3/papers.cfm?abstract id=1004313.

(67.) This discussion assumes that the amount of bureaucratic preference change is a linear function of the number of political capital units that the president devotes to bureaucratic control. That assumption is implicit in the formal model in the Appendix. One might argue, however, that if the bureaucracy also faces increasing marginal costs from undesirable policy outcomes, then the bureaucracy would resist change more strenuously when the president tries to shift the bureaucracy a greater distance from its initial ideal point. If so, this would strengthen the case for assuming that the president faces increasing marginal control costs, because greater bureaucratic resistance likely translates into higher presidential control costs.

(68.) The only case in which this would not be true is the unrealistic special case in which the president places an equal value on all possible alternative uses of her resources.

(69.) In the formal analysis, the final policy, [x.sub.1], is equal to [b.sub.1], and each player's final utility payoff from the policy outcome is equal to the negative square of the distance between the player's ideal point ([v.sub.1] or [p.sub.1]) and the final outcome ([x.sub.1]). See infra Section A of the Appendix.

The assumption that political actors have concave utility functions is standard in the political science literature; the assumption that this function is quadratic is a conventional simplification typically justified on grounds of mathematical convenience. See JAMES M. ENELOW & MELVIN J. HINICH, THE SPATIAL THEORY OF VOTING 81-82, 165 (1984). Some have questioned, however, whether the concavity assumption makes sense when the relevant "good" is a policy outcome. See ELHAUGE, supra note 17, at 349 n.79.

In the context of regulatory policy, one might defend the concavity assumption on the following grounds: A political actor's ideal regulatory policy (e.g., the ideal stringency of a safety standard) is determined by the point at which the regulation's marginal benefit equals its marginal cost. Even if one assumes that the regulation's marginal benefits are constant (each life saved counts just as much, no matter the total number of lives saved), the regulation's marginal cost is likely to be increasing, because social resources devoted to increased safety will tend to be diverted from low-value uses before they are diverted from high-value uses. See supra text accompanying notes 67-58. For this reason, an actor's net cost from policies that deviate from her ideal point will increase--at an increasing rate--as the size of the deviation gets larger. This implies a concave utility function.

To illustrate, suppose that the regulatory benefit is defined in terms of number of statistical lives saved and the regulatory cost is the opportunity cost of lost economic productivity. Suppose that, for a given actor, the benefit of the regulation, in units of utility, is equal to 10 x (number of lives saved), while the cost is equal to (number of lives saved) (2). This means the marginal benefit is constant at 10, while the marginal cost is equal to 2 x (number of lives saved). The actor's ideal regulatory policy is one that saves five lives, because at this point the marginal cost equals the marginal benefit (both are equal to 10); at this point, the actor's net utility is 25 (50-25). If the regulation were more stringent, so that it saves six lives--one more than the actor's ideal policy--the actor would receive a final utility of 24 (60-36). If the regulation were still more stringent, so that it saves seven lives, the actor's final utility would be 21 (70-49). The results are symmetric for deviations below rather than above the actor's ideal level of regulatory stringency: If the regulation saves four lives, her utility is 24 (40-16); if it saves three lives, her utility is 21 (30-9). Thus a deviation of two "units" (statistical lives saved) from the actor's ideal point is more than twice as bad, in utility terms, as a deviation of one unit. This is consistent with the concavity assumption.

That said, there may be regulatory policy issues where the concavity assumption is more difficult to justify, especially when neither the regulatory benefits nor the costs can be readily conceived as the opportunity cost of diverting social resources from some other use. The analysis presented in this Article should be treated with caution in such contexts.

(70.) The formal analysis of this case is presented in Section B.2 of the Appendix.

(71.) The analysis in this Section would be the same in all substantive respects if the bureaucracy's ideal point were located to the voter's left.

(72.) This formulation is potentially misleading; the president always wants to move the bureaucracy toward her own ideal point. That said, when we observe an administration to the right of the median voter attempting to shift policy in a leftward direction, or vice versa, we should expect these to be precisely the cases in which voters are most sympathetic to broad claims of presidential authority.

(73.) The formal analysis of this case is presented in Section B.3 of the Appendix.

(74.) For a discussion and justification of the assumption that marginal control costs are increasing in the magnitude of the policy change, see supra text accompanying notes 66-68.

(75.) Speaking more technically, the curve depicted by the dashed line in Figure 3 is the probability density function for the president's ideal point.

(76.) The example in the text does not correspond exactly to the median voter's optimal level of bureaucratic insulation. The expected divergence between the outcome and the voter's ideal point is even lower when the president moves EPA policy approximately 75.257% of the way toward the president's ideal point. Also, if the voter views the marginal cost of policy divergence as increasing in the size of the divergence (the assumption made in the formal analysis), optimal bureaucratic insulation will be higher. The discussion in the text neglects these complications in order to illustrate the basic intuition with a relatively simple example.

(77.) Importantly, this result does not depend on the assumption that the voter is risk averse, though risk aversion might supply a separate reason why a voter might prefer a more biased expected policy outcome with lower variance to a less biased policy outcome with higher variance. Even a risk-neutral voter treats the variance of policy outcomes as a cost because higher variance implies a higher expected distance between the policy ultimately chosen and the voter's ideal point. Indeed the textual examples do not assume risk-averse voters (though the formal analysis in the Appendix does). The only situation in which the basic result does not hold with a risk-neutral voter is when there is zero probability that the actual outcome will fall on the opposite side of the voter's ideal point as the expected outcome.

(78.) These results are related to Neal Katyal's advocacy of an "internal separation of powers" within the executive branch, including mechanisms that give agencies more autonomy from direct political control. See Katyal, supra note 9. Katyal, however, bases his arguments for bureaucratic autonomy primarily on his claims that such autonomy improves the quality of information and that bureaucrats may take a longer-term view of the national interests. This Article shows that some degree of bureaucratic insulation is desirable for a majority of voters even if bureaucratic insulation confers no informational benefits and even if bureaucrats do not seek to maximize long-term national welfare.

(79.) These comparative results follow directly from Equation (9) in the Appendix.

(80.) See Kagan, supra note 22, at 2341-46; Cass R. Sunstein, National Security, Liberty, and the D.C. Circuit, 73 GEO. WASH. L. REV. 693, 702 (2005).

(81.) See ROBERT S. ERIKSON ET AL., THE MACRO POLITY 256-69, 309-11 (2002); MORRIS P. FIORINA, CULTURE WAR? THE MYTH OF g POLARIZED AMERICA 16-21 (2d ed. 2006); Joseph Bafumi & Michael C. Herron. Preference Aggregation, Representation, and Elected American Political Institutions (Dec. 18, 2007) (unpublished manuscript), available at http://www.dartmouth.edu/~herron/RepInstitutions.pdf; cf. Michael A. Bailey, Comparable Preference Estimates across Time and Institutions for the Court, Congress, and Presidency, 51 AM. J. POE. SCI. 433 (2007) (finding substantial divergence in the policy preferences of presidents from different parties, as well as substantial divergence between the ideal point of presidents and median legislators); Michael Bailey & Kelly H. Chang, Comparing Presidents, Senators, and Justices: Interinstitutional Preference Estimation, 17 J.L. ECON. & ORG. 477 (2001) (reaching similar conclusions); Charles R. Shipan & William R. Lowry, Environmental Policy and Party Divergence in Congress, 54 POL. RES. Q. 245 (2001) (finding that Republicans and Democrats take substantially different positions on environmental policy issues).

(82.) The finding that the positions of elected politicians systematically diverge from the median voter's ideal point, though inconsistent with the simplest spatial models of electoral competition, is consistent with more sophisticated models that incorporate factors like incomplete information, differential voter activism, and politicians' personal policy goals. See Peter H. Aranson & Peter C. Ordeshook, Spatial Strategies for Sequential Elections, in PROBABILITY MODELS OF COLLECTIVE DECISION MAKING 298 (Richard G. Niemi & Herbert F. Weisberg eds., 1972); Randall L. Calvert, Robustness of the Multidimensional Voting Model: Candidate Motivations, Uncertainty, and Convergence, 29 AM. J. POL SCI. 69 (1985); Susanne Lohmann, An Information Rationale for the Power of Special Interests, 92 AM. POL SCI. REV. 809 (1998); Rebecca B. Morton, Incomplete Information and Ideological Explanations of Platform Divergence, 87 AM. POL. SCI. REV. 382 (1993).

(83.) See Joshua D. Clinton & David E. Lewis, Expert Opinion, Agency Characteristics, and Agency Preferences, 16 POL. ANALYSIS 3 (2008) (using expert opinion surveys to assess long-term agency ideological leanings and finding that although some agencies consistently slant liberal or conservative, most appear relatively moderate); David C. Nixon, Separation of Powers and Appointee Ideology, 20 J.L. ECON. & ORG. 438 (2004) (finding that the confirmation process tends to result in agency heads who are more moderate than the appointing president); see also Dan Ho, Measuring Agency Preferences: Expert Surveys, Agency Voting, and the Influence of the Chair (Aug. 16, 2007) (unpublished manuscript), available at http://dho.stanford.edu/ research/fccsurvp.pdf (discussing empirical techniques for estimating the ideal points of agency officials).

(84.) See ERIKSON ET AL., supra note 81, at 256-69; Stephen Ansolabehere, Jonathan Rodden & James M. Snyder, Jr., Issue Preferences and Measurement Error (Jan. 2006) (unpublished manuscript), available at http://web.mit.edu/polisci/portl/cces/material/ ansolabehere_rodden_snyder.pdf.

(85.) This extension is presented formally in Section C.1 of the Appendix. The relative weight the voter places on presidential control costs is parameterized as [lambda]. See infra Section C.2 of the Appendix.

(86.) There is also a fourth case, in which the voter and the president place the same relative value on policy outcomes and control costs. As the Appendix shows, the results in this case are equivalent to those in the second case, where the voter places a higher relative weight on control costs than does the president. See infra Section C.1 of the Appendix.

(87.) A final issue to consider is the potential relationship between expected presidential responsiveness on the bureaucratic policy issue and the degree to which presidential control efforts impose costs on the voter. These might be positively correlated. After all, if the institutions designed to promote political accountability are working well, we might expect a high degree of expected presidential responsiveness both on the bureaucratic policy issue and other issues to which the president might devote her scarce resources. This possibility, considered in more detail in Section C.I of the Appendix, introduces some additional complexity, but it does not change the central qualitative results.

(88.) This extension is presented formally in Section C.2 of the Appendix. The efficacy of direct monitoring is formalized as the difference between the variance of the president's ideal point under low scrutiny ([[sigma].sup.2.sub.L]) and high scrutiny ([[sigma].sup.2.sub.H]). The cost to the voter of high scrutiny is parameterized as [kappa]. See infra Section C.2 of the Appendix.

(89.) See SCHOENBROD, supra note 13. at 14.

(90.) This extension is presented in Section C.3 of the Appendix. The expected presidential bias selected by the voter is denoted [mu].

(91.) This extension is presented formally in Section C.4 of the Appendix. The second policymaking stage is denoted as period t=2. The voter's period 2 ideal point is [v.sub.2]=[v.sub.1]+[[epsilon].sub.2], where [[epsilon].sub.2] is an independent draw from a distribution with mean 0 and variance [[rho].sub.2]. The president's period 2 ideal point is [p.sub.2]=[v.sub.2]+[[alpha].sub.2], where [[alpha].sub.2], is an independent draw from a distribution with mean 0 and variance [[sigma].sup.2]. See infra Section C.4 of the Appendix.

The assumption that the voter's total utility is the sum of her utility in each stage implies that, from the voter's perspective, policy excesses in one direction would not be offset by equivalent excesses in the opposite direction in subsequent stages (either naturally or through some sort of compensatory action by the voter). This assumption might be problematic in some cases. For instance, if the policy dimension is the aggressiveness of law enforcement activity, then perhaps the voter might care only about the average long-term deterrent effect and the long-term average enforcement cost, but the voter might not care about short-term fluctuations in the level of aggressiveness. If the voter cares only about the average policy outcome over time then the voter would prefer maximum presidential control. This criticism, however, undermines this Article's main findings only in the extreme case in which the voter cares solely about the over-time average policy position. As long as the voter cares at least somewhat about the within-period policy outcome, then the voter is willing to accept some level of policy bias in order to reduce outcome variance. The extreme assumption that voters care only about the long-term average policy outcome appears substantively implausible in most cases. That said, this critique suggests another comparative hypothesis. The more the voter cares about within-period outcomes, relative to the average overall outcome, the higher the voter's optimal level of insulation. Therefore, in policy domains where the long-term average policy outcome is relatively more important to voters' utility, the optimal level of bureaucratic insulation will be lower, all else equal; in domains where voter utility turns more on the currently prevailing policy, optimal bureaucratic insulation will tend to be higher.

(92.) Cf. Nina A. Mendelson, Agency Burrowing: Entrenching Policies and Personnel Before a New President Arrives, 78 N.Y.U.L. REV. 557 (2003) (describing and assessing the phenomenon of "agency burrowing," in which presidents take actions late in their terms designed to have lasting effects on agency policy preferences).

(93.) See Calabresi, supra note 20, at 69-70 & n.114.

(94.) In the particular example elaborated in the main analysis, this separation of powers is an "internal" separation within the executive branch. Cf. Katyal, supra note 9.

(95.) One position holds that Congress prefers administrative structures and processes that insulate agencies from ongoing congressional influence, because members of the enacting coalition want to "lock in" policy gains by rendering their decision harder to undo by future Congresses. See Mathew D. McCubbins, Roger G. Noll & Barry R. Weingast, Structure and Process, Politics and Policy: Administrative Arrangements and the Political Control of Agencies, 75 VA. L. REV. 431 (1989); Terry M. Moe, The Politics of Bureaucratic Structure, in CAN THE GOVERNMENT GOVERN? 267 (John E. Chubb & Paul E. Peterson eds., 1989); Terry M. Moe, The Politics of Structural Choice: Towards" a Theory of Public Bureaucracy, in ORGANIZATION THEORY 116 (Oliver E. Williamson ed., 1990). Attempts to model this "policy insulation" theory formally have yielded important limitations and qualifications. See Rui J. P. de Figueiredo, Jr., Electoral Competition, Political Uncertainty, and Policy Insulation, 96 AM. POL. SCI. REV. 321 (2002). An alternative perspective argues that Congress chooses structures and processes to maximize Congress's ability to monitor agencies on an ongoing basis. See Bressman, supra note 17; McCubbins, Noll & Weingast, supra; Mathew D. McCubbins & Thomas Schwartz, Congressional Oversight Overlooked: Police Patrols versus Fire Alarms, 28 AM. J. POL. SCI. 165 (1984). Interestingly, these hypotheses are sometimes bundled together, even though they seem to be in some tension with each other.

(96.) See James R. Rogers, Information and Judicial Review: A Signaling Game of Legislative-Judicial Interaction, 45 AM. J. POL. SCI. 84 (2001); Eli M. Salzberger, A Positive Analysis of the Doctrine of Separation of Powers, or: Why Do We Have an Independent Judiciary?, 13 INT'L REV. L. & ECON. 349 (1993); Matthew C. Stephenson, Court of Public Opinion: Government Accountability and Judicial Independence, 20 J.L. ECON. & ORG. 379 (2004); Matthew C. Stephenson, "When the Devil Turns ...": The Political Foundations of Independent Judicial Review, 32 J. LEGAL. STUD. 59 (2003).

(97.) The analysis is robust to allowing for random variation in the bureaucracy's ideal point prior to presidential action. To see this, assume that the voter's period 1 ideal point is [v.sub.j]=[v.sub.0]+[[epsilon].sub.v] and that [epsilon], is a random draw from some distribution with mean 0 and variance [[rho].sup.2.sub.v]. (Note that the only change so far is the addition of the v subscripts.) Next, assume that the bureaucracy's ideal point at the start of period I is [b.sub.1],=[b.sub.0] + [[epsilon].sub.b], where [[epsilon].sub.b], is a random draw from some distribution with mean 0 and variance [[rho].sup.2.sub.b]. We can redefine [[epsilon].sub.1] as equal to ([[epsilon].sub.v] - [[epsilon].sub.b]). The mean of this distribution is 0. The variance, which we can denote by [[rho].sup.2] as in the main text, is E([[epsilon].sub.v.sup.2] + [[epsilon].sub.b.sup.2])- E[([[epsilon].sub.v] - [[epsilon].sub.b]).sup.2] = [[rho].sub.v.sup.2] + [[rho].sub.b.sup.2]- 2cov([[epsilon].sub.v][[epsilon].sub.b]). While the main exposition and analysis assumes that [[rho].sup.2.sub.b]=0 (or that cov([[epsilon].sub.v][[epsilon].sub.b])=[[rho].sub.b.sup.2]/2, the results can easily be extended to incorporate the possibility of a randomly shifting bureaucratic ideal point.

(98.) We can verify that [[beta].sup.*] maximizes the voter's expected utility by taking the second derivative with respect to [beta]:

[d.sup.2][EU.sup.V.sub.1] / d[[beta].sup.2] = -2([[rho].sup.2] + [[sigma].sup.2] + [b.sub.0.sup.2]) < 0

(99.) We can verify that this expression maximizes rather than minimizes the voter's expected utility by taking the second derivative with respect to [beta]:

[d.sup.2][EU.sup.V.sub.CE] = -2 (1 - [lambda])([[sigma].sup.2] + [[rho].sup.2] + [b.sub.0.sup.2]) < 0

(100.) See supra note 98.

(101.) This assumption rules out the more complicated but potentially interesting scenario in which presidents deliberately try to influence bureaucratic policy choices in subsequent periods, or where the bureaucracy tries to strategically shield its current policies from future influence.

Matthew C. Stephenson, Assistant Professor of Law, Harvard Law School. I am grateful to David Baron, Ryan Bubb, Lisa Bressman, Einer Elhauge, Dick Fallon, Charles Fried, Barry Friedman, Jake Gersen, Jim Greiner, Howell Jackson, Elena Kagan, Louis Kaplow, Daryl Levinson, Katerina Linos, John Manning, Dan Meltzer, Tom Merrill, Martha Minow, Jide Nzelibe, Eric Posner. Ricky Revesz, Bill Stuntz, Adrian Vermeule, Judge Stephen Williams, Alan Wiseman, John Yoo, and workshop participants at Harvard Law School, UC Berkeley School of Law, Northwestern University Law School, Florida State University College of Law, the Harvard-MIT Political Economy Colloquium, the Stanford/Yale Junior Faculty Forum, and the Emory Institute for Law, Politics, and Economics for helpful comments and conversations.
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