Absence of Envy Does Not Imply Fairness: Reply.

Randall G. Holcombe [*]

1. Introduction

I titled my reply using the title of my original paper rather than the title of Berliant, Thomson, and Dunz's comment, "On the Fairness Literature," because my 1997 paper dealt only with the issue in its title, not with the fairness literature in general. What I intended to show was only that the statement in the title is true: Absence of envy does not imply fairness. I want to do two things in this reply: first, consider the claim I made in the title of my original paper in light of the comment of Berliant, Thomson, and Dunz, and second, respond to the issues they raised in their comment. I will be brief in supporting my original claim, because Berliant, Thomson, and Dunz do not dispute it. Nowhere do they argue that any part of my paper is incorrect, but rather, they say, "Holcombe's exclusive focus on the no-envy solution is not warranted." Thus, we appear to be in agreement that my original paper demonstrated that the absence of envy does not imply fairness, as its title claimed, and that my original pap er focused exclusively on the no-envy criterion. We agree on something else too. In my original paper, I quoted Berliant, Thomson, and Dunz (1992, p. 202), and in their comment, they also quoted themselves as having said, "There now exists in economics a well-developed literature devoted to the formulation and the analysis of equity concepts. The concept that has played the central role is that of an envy-free allocation." Thus, we also agree that the concept of an envy-free allocation is the central concept in this literature.

I did not write my original paper as a comment on Berliant, Thomson, and Dunz (1992), or any other specific paper, or on the fairness literature in general; rather, I hoped to make an independent contribution to this literature with a clear and convincing demonstration that the absence of envy does not imply fairness, even in the most straightforward case. The reason I cited Berliant, Thomson, and Dunz was to show that some of the most frequent contributors to this literature [1] believe that the concept I focused exclusively on is, in fact, the central concept in the fairness literature. Academic writing often focuses on very narrow concepts to get a better idea of their properties and implications, and my exclusive focus on the concept that Berliant, Thomson, and Dunz call the central concept in the fairness literature does not seem inappropriate, especially when that narrow focus demonstrates that the central concept in the fairness literature is neither necessary nor sufficient to ensure fairness. [2]

2. Limitations of the Fairness Literature

Berliant, Thomson, and Dunz say I raise four criticisms of the fairness literature, but in fact I make only one, and I prefer to consider it an observation, not a criticism. Also, as I noted in my 1997 paper, many other contributors to the literature have made the same observation. Consider the criticisms they list.

First, they list as a criticism my observation that an allocation may be envy-free but not fair. Defending the fairness literature against my observation, they note that the literature has examined many other criteria, and I am happy to acknowledge that this is the case. However, my paper dealt only with the no-envy criterion. My paper was not an attack on the fairness literature but rather was limited to an analysis of what Berliant, Thomson, and Dunz call the central concept of that literature.

Second, they say I criticize the literature because "some agents may deserve more than others, and envy might well be justified then." Here again, we agree that this is true, but I did not intend it as a criticism of the fairness literature. Rather, I noted that others in the literature have already analyzed situations in which some might deserve more than others, and in such cases, fair outcomes may not be envy-free. For that reason, the analysis in Holcombe (1997) takes place in a purely distributional framework where nobody deserves more than anybody else, so this issue is irrelevant to my analysis. My point was that even in a situation where nobody is more deserving than anybody else, an envy-free outcome still can be shown to be unfair. I brought up the issue of merit not as a criticism of the fairness literature, but rather to point out that it is not relevant to my 1997 analysis of envy-free outcomes.

Third, they say I criticize the literature because "random devices may appear fair, but once implemented they are not." Again, we agree on this, and I was not criticizing the literature because of it. My original example does not rely on random devices, and I brought this up in my 1997 paper only to show that one cannot escape from my conclusion by appealing to the possibility of adding random devices to the mechanism in my paper. As I noted in my 1997 paper, some authors have employed random devices to try to avoid just the problem that paper addresses, so I believed it was worth discussing--not as a criticism of the literature but to show that it is irrelevant to the problem at hand.

Fourth, they say I criticize the literature by saying, "The fairness of the process that leads to the final allocations should not be ignored." I agree with that statement, and that was my main point in Holcombe (1983). I do not view this as a criticism of the literature, which has recognized this point, but rather brought it up because the reason Holcombe (1997) concludes that absence of envy does not imply fairness is that the process for producing an envy-free outcome can be biased to favor some individuals over others. This is relevant because the freedom-from-envy criterion is an evaluation of an outcome and does not take into account the process that produces an envy-free outcome. The point is relevant, but I did not raise it as a criticism of the literature. My only goal in my original paper was to demonstrate that the absence of envy does not imply fairness.

3. Conclusion

Berliant, Thomson, and Dunz are critical of the narrow focus of my 1997 paper, but in closing, it is worth repeating those things on which we appear to agree so it is clear where any differences between us begin. We all agree that absence of envy does not imply fairness; my original paper focused exclusively on the no-envy criterion; and the no-envy criterion plays the central role in the fairness literature. My 1997 paper was not intended as a comment on Berliant, Thomson, and Dunz (1992), but I see how they could have taken it as such. The title of their paper says it is about "fair division," but on pages 203-4, they say, "We now present our main equity notion.... a partition is envy-free if no agent would prefer someone else's parcel to his own. This concept is the central one in the economics literature." Nowhere after this equity notion is presented to the reader does their paper ever mention fairness, not even in the conclusion. Thus, I would argue that their paper is about envy-free division, not fai r division, and that the two are not the same.

In my 1997 paper, I cited a number of contributions to the literature that discussed problems with equating fairness and freedom from envy, and I am happy to acknowledge that there is a broader literature on the subject. At the same time, I believe that sometimes the freedom-from-envy concept has been inappropriately relied on as an indicator of fairness in that literature. Thus, I will close by re-emphasizing the only point I intended to make in my original paper, and a point on which both my critics and I appear to agree: Absence of envy does not imply fairness.

(*.) Department of Economics, Florida State University, Tallahassee, FL 32306, USA; E-mail [e-mail].

(1.) By my count, Berliant, Thomson, or Dunz are authors or coauthors of 18 of the 63 references they cite in their comment on the fairness literature, or about 29% of the total.

(2.) Could Berliant, Thomson, and Dunz (1992) be vulnerable to the same criticism they level at me? Their 1992 paper analyzes only two equity criteria: no envy and egalitarian equivalence. Although this is twice the number of equity criteria I examine, one still might argue that in light of the voluminous literature cited in their comment, their exclusive focus on only these two criteria is unwarranted. My point is that any one paper always has a narrower focus than a body of literature consisting of hundreds of articles and books.

References

Berliant, Marcus, William Thomson, and Karl Dunz. 1992. On the fair division of a heterogeneous commodity. Journal of Mathematical Economics 21:201-16.

Holcombe, Randall G. 1983. Applied fairness theory: Comment. American Economic Review 73:1153-6.

Holcombe, Randall G. 1997. Absence of envy does not imply fairness. Southern Economic Journal 63:797-802.