Pairwise Justifiable Changes in Collective Choices

Abstract

Consider the following principle regarding the performance of collective choice rules. "If a rule selects alternative x in situation 1, and alternative y in situation 2, there must be an alternative z, and some member of society whose appreciation of z relative to x has increased when going from situation 1 to situation 2." This principle requires a minimal justification for the fall of x in the consideration of society: someone must have decreased its appreciation relative to some other possible alternative. On appropriately restricted domains, pairwise justifiability, along with anonymity and neutrality, characterizes Condorcet consistent rules, thus providing a foundation for the choice of the alternatives that win by majority over all others in pairwise comparisons, when they exist.

We study the consequences of imposing this requirement of pairwise justifiability on a large class of collective choice rules that includes social choice and social welfare functions as particular cases.

When preference profiles are unrestricted, it implies dictatorship, and both Arrow's and the Gibbard-Satterthwaite's theorems become corollaries of our general result.

Keywords: Pairwise justifiability, social choice functions, social welfare functions, Condorcet consistency, Arrow's theorem, Gibbard-Satterthwaite's theorem

JEL Classification: D70, D71, D78