Absence of Envy Does Not Imply Fairness: Reply.

• Author: Holcombe, Randall G.

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...