A short proof of Deb's Theorem on Schwartz's rule

摘要

Schwartz in (Nous,7,1972, Definition, 3) introduces a generalization of the Condorcet criterion, which is the classical approach to rational choice in the context of cycles, and he defines the Schwartz set. Deb (J Econ Theory 16:103-110, 1977) shows that the Schwartz set consists of the maximal elements according to the transitive closure of the asymmetric part of a binary relation corresponding to a choice process or representing the decision maker's preferences. This note provides a short and simple proof of Deb's theorem on the characterization of the Schwartz set.