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Agendas and strategic voting.

1. Introduction

In traditional economics classes, students learn that the independent actions of consumers and producers can lead to efficient market outcomes.(1) In a democracy, however, decisions are often made collectively, and the political process can result in a set of programs with costs that far exceed benefits. Conversely, projects with very high benefits to a minority of voters can go unfunded in the absence of logrolling. Outcomes can vary widely, depending on the institution in place. With majority rule, for example, voters can strategically manipulate the agenda to favor certain outcomes.

This paper provides the setup for a classroom experiment in which several proposals are considered in sequence and coalitions can approve a set of policies with a net loss to society. Pairwise votes between alternatives can result in cycling, in which case the order of votes determines the final outcome. As voters become aware of this, attempts to control the agenda can occur. This exercise stimulates discussions of political institutions, strategic voting, and the size of government. The exercise can be used to supplement chapters on the role of government or public choice in introductory or intermediate microeconomics classes. It can also be used in more specialized topics courses, such as public economics or law and economics.
Table 1. Voters' Card Allocations

V1 V2 V3 V4 V5 V6 V7

Heart Heart Heart Heart Club Club Club
Spade Spade Club Club Spade Spade Spade

Highway Highway Highway Highway School School School
School School

2. Procedures

The exercise can be done with as few as seven students and will take from 30 to 45 minutes. You will need one deck of cards for as many as 14 people and two decks for as many as 35 people. Cards are distributed to voters in the manner described below, and the suit of a card determines the voter's preferences. A voter who receives a Heart has a preference for the "highway" project, and a voter who receives a Spade has a preference for the "school" project. A Club card has no effect on preferences. Each voter receives two cards, and therefore some might prefer to see both projects funded; however, no one benefits twice from one project. For each group of seven voters labeled VI to V7, the cards should be distributed as shown in Table 1. Note that the Club cards are neutral. Voters can be added in multiples of seven by replicating the above allocations. When the number of students in a class is not an exact multiple of seven, let some students sit together in pairs and act as a single voter. The numbers on the cards do not matter, and therefore you can combine two decks to get 26 Spades, which will accommodate five replications of the seven-voter profile. Finally, it speeds things up to sort the cards in advance and put them into envelopes.

The instructions in the appendix explain how payoffs are determined. Each voter pays a tax of $200 for each project that is funded. The benefit of a school is $300 for a voter with a Spade, and the benefit of a highway is $300 for a voter with a Heart. For example, if both projects are funded, voters VI and V2 earn $600 in benefits minus $400 in taxes, and all other voters earn $300 in benefits minus $400 in taxes. Notice that five voters favor the school, so its aggregate benefit, 5 x 300 = $1,500, exceeds the cost of 7 x 200 = $1,400. The highway, on the other hand, has an aggregate benefit of 4 x 300 = $1,200, which is less than the aggregate cost of $1,400. Finally, the aggregate benefits of the highway/school package, $2,700, are less than the aggregate costs of the package: $1,400 x 2 = $2,800.

These payoffs make it possible to observe a voting cycle in which one option beats a second, which beats a third, which in turn beats the first one. In a choice between neither project and the highway by itself, the highway wins with the support of voters V1 to V4. In a choice between the highway by itself and both projects, the two-project package wins. This is because voters V1 and V2 benefit from both projects, and voters V5, V6, and V7 prefer the -$100 from the two-project package to the -$200 from the highway only. To complete the cycle, note that funding neither receives more votes than funding both. (The only voters who prefer both to neither are those who receive both a Heart and a Spade.)

Agenda 1 in the appendix is designed to lead students through a cycle. This agenda also shows how each project can be funded when considered one at a time in sequence, although most prefer to fund neither rather than both. The results of agenda 1 can be recorded by writing the vote totals on the blackboard: Highway XX versus No Highway XX; School XX versus No School XX, Funded Projects XX versus Neither XX. Agenda 2 leads the students back through [TABULAR DATA FOR TABLE 2 OMITTED] the cycle in pairwise comparisons of possible options. Agenda 3 is a commonly used setup where voters choose between two challengers in the first stage (primary) and then between the winner and a third option, the status quo, in a runoff. This agenda also illustrates the difference between naive and strategic voting, as discussed in the next section. If there is no strategic voting in agenda 3, you can allow students to discuss strategies before repeating the sequence of votes in agenda 3 a second time.

Depending on class size and probable attendance, arrange the cards in order so you can give the top two cards to the voter who corresponds to V1, the next two cards to the voter who corresponds to V2, and so on. You can use rubber bands to separate the groups of 14 cards that go to each set of seven voters. If the number of students present is not a multiple of seven, let some of the excess students work in pairs, but each pair only has a single vote.

At the start of class, pass out the instructions, distribute the cards, read the instructions out loud, and answer any questions that arise. Read each agenda as you proceed, and make sure that students record their votes and earnings. To facilitate later discussions, keep track of the vote outcomes on the blackboard. People who abstain from voting will not cause a problem in a large class, but abstentions should not be allowed in a small class (seven people), where vote counts are likely to be close. You can increase interest by announcing that one student will be selected at random, ex post, to be paid 1% of earnings plus $4.(2)

3. Discussion

Before beginning the discussion, put the seven-voter distribution of cards on the blackboard and explain that the classroom exercise used a multiple of this setup. The discussion of results can be organized around the agendas. Results from a session conducted in a public economics class at American University are presented in Table 2. The seven-card setup described here was replicated three times to accommodate 21 students.

In Vote 1 of agenda 1, "Raise your hand if you want to fund the highway," there were 13 yes votes. The school project was also funded (in vote 2) with 16 yes votes. The discussion here should focus on how sequential majority voting can lead to a package of projects with a positive net benefit for a minority (6 out of 21). In the final vote of agenda 1, Neither defeated the package of projects previously approved. This completed the voting cycle. Ask students to think of some realistic examples where sequential voting leads to a set of funding decisions that would not survive a referendum on the package as a whole (e.g., spending and tax-reform propositions).

Recall that there were 13 votes in favor of the highway in vote 1 of agenda 1, despite the fact that only four of each seven voters (in this case, 12 of 21) had highway cards. Similarly, someone without a school card voted to fund it in vote 2. You should encourage a discussion of this pattern if it emerges. In this class, one person without a highway card voted to fund the highway because he thought it would help many of his classmates. The comments of other students also suggested altruism or reciprocity, and someone admitted that he made a mistake.

Agenda 2 is one in which the winner at one stage is matched against a new alternative in the next stage, as shown in Table 1. Because Neither beats Both in the final stage of agenda 1, agenda 2 started with Neither, which lost to Highway Only, which in turn lost to School Only. Finally, School Only lost to Both, which again illustrates how pairwise majority voting can result in a package funding decision that benefits only a minority. (Because voters V1 and V2 are indifferent between Highway Only and School Only, it is possible that Highway Only will win in vote 2.) In any event, Both should prevail in vote 3. The point here is not that majority voting necessarily results in an inefficiently high level of spending but that this can happen for particular preferences and agendas.

The order of votes determines the outcome, and to emphasize this ask students to design an agenda in which School Only (or some other outcome) will be selected. They will quickly discover that there are many different ways to obtain each potential outcome. Again, have them think of actual situations where agenda manipulation might arise.(3)

Agenda 3 gives students an opportunity to vote strategically, that is, against their preference in an early stage to affect the choices and outcomes in later stages. In contrast, voting strictly in accordance with one's preference in the current stage will be called naive, or sincere, voting. In vote 1 of agenda 3, there is a runoff between two challengers: School Only and Neither. The winner is then paired against the status quo, which is Both. Note that naive voting results in School Only winning vote 1 and Both beating School Only in vote 2 by a vote of only four to three, so the strategic outcome is less likely in small classes. Only people with both school and highway cards have a net gain from funding Both, so most people would have been better off funding Neither. If enough of these people vote for Neither in vote 1, it will win and subsequently beat Both in vote 2. It is unlikely that students will vote strategically at first.(4) Note from Table 1 that only the six students who benefited exclusively from the highway voted for Neither in vote 1 of agenda 3. We also observed very little strategic voting when agenda 3 was used with a group of 35 economics professors and graduate students. Only 3 of the 9 voters who should have voted strategically for Neither in vote 1 actually did so.(5) Agenda 3 is analogous to a presidential primary, in which one can vote against one's preferred candidate to help a candidate who is expected to be weak against one's second-favorite candidate.

To promote strategic thinking, allow some class discussion after agenda 3 but before agenda 4, which is a repeat of agenda 3. In the experiment summarized in Table 1, a few students recognized this strategy during the discussion and explained it to the others. Therefore, Neither won vote 1 in agenda 4 and proceeded to defeat Both in vote 2. Students with both highway and school cards were very unhappy with the class discussion and made a motion to terminate the discussion and proceed with the vote before doubters could be convinced that voting for Neither in the first round was the best strategy.(6) Some classes will simply not produce a strategic outcome, especially groups of seven voters, where one mistake can change the vote outcome. The fragility of the result of agenda 3 might be due in part to the fact that School Only increases net surplus, and voters 1 and 2 with both highway and school preferences might not care much in the second-stage vote between School Only (where they earn $100) and Neither (where they earn nothing). If monetary incentives are not being used, students might be thinking more in terms of earning more than the others, which is not as likely with negative or zero earnings.

The implications of strategic voting can be addressed by asking students whether the agenda that they designed earlier to achieve a specific outcome would still succeed if voters were strategic. Finally, you should ask what characteristics of a committee or organization might make strategic voting more likely. Ask for examples, such as the case of a department meeting with faculty who know a lot about one another's preferences on the basis of a series of votes on similar issues in the past.

4. Further Reading

Much of the public choice literature on voting and resource allocation was stimulated by Buchanan and Tullock's (1962) classic book The Calculus of Consent. Mueller (1989) surveys the literature on voting mechanisms, that is, majority rule and alternatives. Voting cycles are discussed in Brams (1976). An especially interesting case of an actual voting cycle is reported in Neufeld, Hausman, and Rapoport (1994).

The first controlled voting experiment with financially motivated subjects is reported in Fiorina and Plott (1978). Levine and Plott (1977) contains a dramatic account of how the authors used an agenda to manipulate the purchase decisions of a private flying club. The prevalence of naive voting in agenda-controlled committee voting experiments is documented in Plott and Levine (1978). Eckel and Holt (1989) report experiments in which strategic voting emerged, but only with sufficient repetition. There are many other types of voting experiments in the economics and political science literatures. For a survey of this literature, see McKelvey and Ordeshook (1990).


This is a simple exercise to illustrate the effects of different political institutions. At this time we will give each of you two playing cards. These cards will determine whether you benefit from a variety of proposals. We will vote to select among the proposals, with majority role being used at each stage of the voting, and ties will be decided by the flip of a coin. There are two potential projects: highway and school. Each project, if adopted, will cost each of you $200 in taxes. The benefits to you depend on which cards you have. If one of your cards is a Spade, you are a school person and will receive a benefit of $300 if a school is built, so the benefit net of your tax share is $300 - $200 = $100. If one of your cards is a Heart, then you are a highway person and will receive a benefit of $300 if the highway is built, again with the benefit net of taxes equal to $100. If you have both a Heart and a Spade, then your net benefit with both projects is $300 - $200 + $300 - $200 = $200. If you do not have a Spade and the group votes only to build a school, your benefit is -$200, the tax cost. Your net benefit is also - $200 if you do not have a Heart and the group votes only to build a highway. Finally, a Club card has no direct effect on your earnings, so if you have a Club and a Spade, you receive a net benefit of $300 - $200 if only a school is adopted and $0 - $200 if only a highway is adopted. Similarly, if you have a Club and a Heart, you receive a net benefit of $300 - $200 if only a highway is adopted and $0 - $200 if only a school is adopted.

At this time, please look at your cards and write down your net earnings for each of the four possibilities:

Highway only: $ _____ - $200 = School only: $ ____ - $200 = Both highway and school: $ ____ - $400 = Neither: $ ____ - $ 0 =

Negative earnings are possible for some voters; losses will be subtracted and gains added to determine total earnings. These earnings are hypothetical and are used for purposes of discussion only (except as noted below).

Agenda 1

The first two votes determine which projects will be options on the final vote. The final vote will determine which projects are funded, and therefore earnings are determined by the final vote.

First, raise your hand if you want to fund the highway.

Your vote: Yes ____ (fund highway)

No (not fund highway)

Next, raise your hand if you want to fund the school, whether or not the highway was funded.

Your vote: Yes ____ (fund school)

No ____ (not fund school)

At this point, we have agreed to fund the following project(s): ____ Finally, we will decide whether to fund this project (or these projects as a package) or to go back to the initial situation of funding neither. First, raise your hand if you prefer to fund neither project. Next, raise your hand if you want to fund the projects(s) approved thus far.

Your vote: Fund neither _____

Fund package _____

Now record your earnings.

Project(s) funded with Agenda 1: _____

Your earnings for agenda 1: $ _____

Agenda 2

We will start over with a new agenda, and your earnings will be calculated in the same way as before but separately from those of agenda 1. (Imagine that you have moved to a new town just in time for the voting.) First, you will choose between neither project or just the highway. Raise your hand if you want to fund only the highway; now raise your hand if you want to fund neither.

Your vote: Fund highway only _____

Fund neither _____

Next, you will choose between _____ (the winner of the previous vote) and to fund the school only. Raise you hand if you want to fund _____ (the winner of the previous vote); now raise your hand if you want to fund the school only.

Your vote: Fund previous winner _____

Fund school only _____

Finally, you will choose between _____ (the winner of the previous vote) and to fund both projects. Raise your hand if you want to fund _____ (the winner of the previous vote); now raise your hand if you want to fund both projects.

Your vote: Fund previous winner _____

Fund both projects _____

Now record your earnings.

Project(s) funded with agenda 2: _____

Your earnings for agenda 2: $ _____

Agenda 3

Your have moved again, and your new town has tentatively approved both the highway and the school. Two alternatives have been proposed: school only or neither project. The voting in agenda 3 will have two stages. In the first stage, you will choose between the two "challenger" proposals: school only and neither project. The winner in the first stage will be paired against the current status quo (fund both projects).

First stage (school only versus neither): Raise your hand if you prefer school only; now raise your hand if you prefer neither.

Your vote: Fund school only _____

Fund neither _____

Second stage (first-stage winner versus both projects): Raise your hand if you prefer _____ (the first-stage winner); now raise your hand if you prefer both projects.

Your vote: Fund previous winner _____

Fund both projects _____

Now record your earnings.

Project(s) funded with agenda 3: _____

Your earnings for agenda 3: $ _____

Agenda 4

Repeat agenda 3.

Project(s) funded with agenda 4: _____

Your earnings for agenda 4: $ _____

Optional payment: Add up earnings from all agendas, substracting losses if necessary, and compute 1% of this amount, which is then added to $4 to determine your total earnings: $ _____. Now I will pick one person at random to be paid his or her earnings in cash.

We wish to thank Susan Laury for suggestions. This project was funded in part by National Science Foundation grant SBR-9617784.

1 For a discussion of market efficiency in a classroom experiment, see Holt (1996). Potential inefficiencies of market allocations could be due to factors such as asymmetric information (Holt and Sherman, in press). Also, for a classroom exercise that illustrates the potential inefficiencies of the voluntary provision of a public good, see Holt and Laury (1997).

2 The additional $4 payment is used to keep earnings positive as losses are possible in each of the four rounds.

3 Levine and Plott (1977) describe a case of agenda manipulation that students will find interesting. The authors were members of a flying club and were selected to he on the committee that determined the agenda to be used in deciding which types of airplanes to purchase. They conducted a survey of members' preferences and then designed the agenda to achieve the configuration of types of planes that they preferred. The votes in the actual meeting went as they had predicted, and the president of the club tried unsuccessfully to deviate from the agenda during the course of the meeting.

4 Eckel and Holt (1989) conducted a series of committee voting experiments with two-stage agendas and three alternative outcomes. They report virtually no strategic votes in the first sequence of votes, even when subjects were given one another's preferences in advance.

5 This session was conducted at a 1997 conference on classroom experiments in Economics at the University of Virginia. The participants came from a number of East Coast colleges and universities. The overall outcomes corresponded to those from the undergraduate class summarized in Table 1. The only noticeable difference was that some of the professional economists sold their votes in the discussion period prior to agenda 4.

6 In a public choice class, you can use this setup to evaluate the effects of alternative voting rules, for example, Borda counts or other rank-based voting rules. Some of these procedures are summarized in Mueller (1989). Fischer (1996) describes a clever classroom experiment involving a rank-order voting scheme in which the alternative with the lowest number of top rankings is eliminated until some alternative has a majority of top rankings among the alternatives not eliminated.


Brams, Steven J. 1976. Paradoxes in politics: An introduction to the nonobvious in political science. New York: Free Press.

Buchanan, James M., and Gordon Tullock. 1962. The calculus of consent. Ann Arbor: University of Michigan Press.

Eckel, Catherine, and Charles A. Holt. 1989. Strategic voting in agenda-controlled committee experiments. American Economic Review 79:763-73.

Fiorina, Morris P., and Charles R. Plott. 1978. Committee decisions under majority rule: An experimental study. American Political Science Review 72:575-98.

Fischer, Alstair J. 1996. Voting as a decision process. Unpublished paper, University of Adelaide.

Holt, Charles A. 1996. Classroom games: Trading in a pit market. Journal of Economic Perspectives 10(1):193-203.

Holt, Charles A., and Susan K. Laury. 1997. Classroom games: Voluntary provision of a public good. Journal of Economic Perspectives 11 (4):209-15.

Holt, Charles A., and Roger Sherman. 1998. Classroom games: A market for lemons. Journal of Economic Perspectives. In press.

Levine, Michael E., and Charles R. Plott. 1977. Agenda influence and its implications. Virginia Law Review 63:561 604.

McKelvey, Richard D. and Peter C. Ordeshook. 1990. A decade of experimental research on spatial models of elections and committees. In Advances in the spatial theory of voting, edited by James N. Enelow and Melvin J. Hinich. Cambridge, UK: Cambridge University Press, pp. 99-144.

Mueller, Dennis C. 1989. Public choice II. Cambridge, UK: Cambridge University Press.

Neufeld, John L., William J. Hausman, and Ronald B. Rapoport. 1994. A paradox of voting: Cyclical majorities and the case of muscle shoals. Political Research Quarterly 47:423-38.

Plott, Charles R., and Michael E. Levine. 1978. A model of agenda influence on committee decisions. American Economic Review 68:146-70.
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Title Annotation:Teaching Economics with Classroom Experiments: A Symposium
Author:Anderson, Lisa R.
Publication:Southern Economic Journal
Date:Jan 1, 1999
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