On the frontier between possibility and impossibility theorems in social choice
Since Arrow's pioneering work the literature on the paradoxa of social choice is largely developed on the question of justification and importance of transitive rationalization of social preference relations. Later, for the sake of axiomatization of transitivity of social preference relations Arrow considered the problem of aggregation in terms of choice functions instead of binary social preference relations. This axiom in the literature is known as the weak axiom of revealed preference. To examine the desirability of this axiom Sen factorized it into two independent consistency conditions which relate pairwise choice with choice from a superset. He argued that while one of these consistency conditions (known as expansion-consistency) can easily be accommodated with other Arrow conditions, the other (known as contraction-consistency) can not. This leads us to conclude that the contraction-consistency condition is the main culprit for the paradoxa in social choice. This paper attempts to make precise the frontier between possibility and impossibility theorems in social choice by showing that some criterion of rejection of some alternative is the critical factor. To be specific, it is shown that the possibility theorems with expansion- consistency conditions together with other Arrow conditions namely the Pareto principle and the independence of irrelevant alternatives disappear and generate a power structure similar to the one discovered by Arrow and others once the aggregation procedures are required to satisfy some criterion of rejection (of at least one alternative in a superset comparison).
scientific article; zbMATH DE number 3843432