On the frontier between possibility and impossibility theorems in social choice
type: Item
instance of: scholarly article
title: On the frontier between possibility and impossibility theorems in social choice
zbMATH Open document ID: 0531.90002
DOI: 10.1016/0022-0531(84)90074-7
author: Taradas Bandyopadhyay
published in: Journal of Economic Theory
publication date: 1984-01-01T00:00:00Z
review text: 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).
Mathematics Subject Classification ID: 91B14
Mathematics Subject Classification ID: 91B08
zbMATH DE Number: 3843432
zbMATH Keywords: transitive preference
zbMATH Keywords: relations
zbMATH Keywords: consistency conditions
zbMATH Keywords: weak axiom of revealed preference
MaRDI profile type: Publication
full work available at URL: 0022-0531(84)90074-7
OpenAlex ID: W1970096581
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description: scientific article; zbMATH DE number 3843432