A simple proof of Sen's possibility theorem on majority decisions
type: Item
instance of: scholarly article
title: A simple proof of Sen's possibility theorem on majority decisions
zbMATH Open document ID: 1154.91377
DOI: 10.4171/EM/8
author: Christian Elsholtz
author: Christian List
published in: Elemente der Mathematik
publication date: 2006-02-08T00:00:00Z
review text: Summary: Condorcet's voting paradox shows that pairwise majority voting may lead to cyclical majority preferences. In a famous paper, \textit{A. K. Sen} [Econometrica 34, 491--499 (1966; Zbl 0149.17003), reprinted in A. K. Sen, Choice, Welfare and Measurement, Oxford: Blackwell; The MIT Press (1982), Harvard University Press (1997)] identified a general condition on a profile of individual preference orderings, called triplewise value-restriction, which is sufficient for the avoidance of such cycles. This note aims to make Sen's result easily accessible. We provide an elementary proof of Sen's possibility theorem and a simple reformulation of Sen's condition. We discuss how Sen's condition is logically related to a number of precursors. Finally, we state a necessary and sufficient condition for the avoidance of cycles, and suggest that, although there is still some logical space between that condition and Sen's sufficient condition, Sen's condition cannot be further generalized in an appealing way.
Mathematics Subject Classification ID: 91B12
zbMATH DE Number: 5004596
MaRDI profile type: Publication
cites work: A Possibility Theorem on Majority Decisions
description: scientific article; zbMATH DE number 5004596