Economics and Philosophy



William Thomson

University of Rochester,


An allocation rule is ‘consistent’ if the recommendation it makes for each problem ‘agrees’ with the recommendation it makes for each associated reduced problem, obtained by imagining some agents leaving with their assignments. Some authors have described the consistency principle as a ‘fairness principle’. Others have written that it is not about fairness, that it should be seen as an ‘operational principle’. We dispute the particular fairness interpretations that have been offered for consistency, but develop a different and important fairness foundation for the principle, arguing that it can be seen as the result of adding ‘some’ efficiency to a ‘post-application’ and efficiency-free expression of solidarity in response to population changes. We also challenge the interpretations of consistency as an operational principle that have been given, and here identify a sense in which such an interpretation can be supported. We review and assess the other interpretations of the principle, as ‘robustness’, ‘coherence’ and ‘reinforcement’.

William Thomson is the Elmer B. Milliman Professor of Economics at the University of Rochester. He is a Fellow of the Econometric Society and a former President of the Society for Social Choice and Welfare. He is the author of Axiomatic Theory of Bargaining with a Variable Number of Agents (Cambridge University Press, 1989), co-authored with T. Lensberg, and of A Guide for the Young Economist (MIT Press, 2001; 2nd edition, 2011). His current research deals with the normative and strategic analysis of resource allocation problems.


  I outlined the main argument developed in this paper at the 7th Conference on Environmental and Resource Economics held in Toulouse (2009), and I thank Stephan Ambec for his invitation. I am grateful for comments to Azer Abizada, Nanyang Bu, Siwei Chen, Jo Cho, Battal Doğan, Eun Jeong Heo, Paula Jaramillo, Özgür Kıbrıs, Juan Moreno-Ternero, Karol Szwagrzak, Rodrigo Velez and Ayse Yazici. I also thank two referees and the Associate Editor of this journal for their very useful suggestions.