A Quest for Fundamental Theorems of Social Choice

Abstract

We explore the frontier between possibility and impossibility results by analyzing different combinations of "pro-socialness" and "consistency" conditions. This exercise delivers stronger versions of four classical impossibility theorems, and offers a thorough understanding of connections among them. We also characterize social choice functions that are "independent of irrelevant alternatives," which makes evident that the fundamental difficulty of social choice lies in "pairwise" consistency requirements. We also introduce a concise pedagogical approach to classical impossibility theorems.

Keywords: Social choice and welfare, Arrow's impossibility theorem, Hansson-Denicol\`o theorem, Muller-Satterthwaite theorem, Gibbard-Satterthwaite theorem

JEL Classification: D7, D70, D71