Individually-Rational Collective Choice under Random Preferences
The series Working Papers on Economics is published by the Office for Economic Studies at the Banco de la República (Central Bank of Colombia). The works published are provisional, and their authors are fully responsible for the opinions expressed in them, as well as for possible mistakes. The opinions expressed herein are those of the authors and do not necessarily reflect the views of Banco de la República or its Board of Directors.
In this paper I consider the following problem: there is a collection of exogenously given socially feasible sets, and for each one of them, each one of a group of individuals chooses from an individually feasible set. The fact that the product of the individually feasible sets is larger than the socially feasible set notwithstanding, there arises no conflict between individuals. Assuming that individual preferences are random, I here characterize collective choices in terms of the way in which individual preferences must co-vary in order to explain them. I do this by combining standard revealed preference theory and its counterpart under random preferences. I also argue that there exist collective choices that cannot be rationalized, and hence that the individual rationality assumption can be refuted.
