Keywords: pairwise justifiability, Social choice functions, social welfare functions, Condorcet consistency, Arrow's theorem, Gibbard- Satterthwaite's theorem
JEL codes: D70, D71, D78
Abstract
Consider the following principle regarding the performance of collective choice functions. "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 also study the consequences of imposing this requirement of pairwise justifiability on a large class of collective choice correspondences that includes social choice and social welfare functions as particular cases. When preference profiles are unrestricted, pairwise justifiability implies dictatorship, and both Arrow's and the Gibbard-Satterthwaite's theorems become corollaries of our general result.
