Dictatorial domains
type: Item
instance of: scholarly article
title: Dictatorial domains
zbMATH Open document ID: 1069.91026
author: Navin Aswal
author: Shurojit Chatterji
author: Arunava Sen
published in: Economic Theory
publication date: 2003-09-21T00:00:00Z
review text: The well known Gibbard Satterthwaite (GS) theorem says that the only social choice function that is Pareto optimal and strategyproof is the dictatorial one, if there are at least 3 alternatives. It is also well known that if the domain of the social choice functions is restricted to, for instance, single peaked preferences, also non dictatorial choice functions may exist. The problem addressed in this paper is: how far can the universal domain of all possible profiles be restricted while still retaining the impossibility result of dictatorship. The main result of the paper is: if the domain \(D\) of strict orderings on \(A\) is linked (and there are at least 3 alternatives), then it is dictatorial, i.e., for all social choice functions \(f: D^{N} \rightarrow A\) satisfying unanimity, if \(f\) is strategyproof, then \(f\) is dictatorial. Linked domains are described as follows. Two alternatives \(a\) and \(b\) are said to be connected if there exists a strict ordering in \(D\) where \(a\) is ranked first and \(b\) second and another one where \(b\) is first and \(a\) is second. A domain \(D\) is linked if one can arrange all the alternatives in a sequence satisfying the following property: the second alternative is connected to the first and every alternative after the second is connected to at least two others before it in the sequence. The assumption that the domain is linked is significantly weaker than the assumption that the domain is universal. Hence, this theorem generalizes the GS theorem. The proof requires about 5 pages. The authors demonstrate the existence of a linked domain which has exactly \(4m - 6\) orderings, where \(m\) is the number of alternatives, while the universal domain is of size \(m!\). The authors apply their main result to a model of voting under constraints, due to Barbera, Sonnenschein and Zhou, intended to represent a situation where members are being elected to a club. A domain \(D\) has the unique seconds property if there exists a p…
Mathematics Subject Classification ID: 91B14
Mathematics Subject Classification ID: 91B12
zbMATH DE Number: 1983470
zbMATH Keywords: domain restrictions
zbMATH Keywords: dictatorship
zbMATH Keywords: strategyproof
zbMATH Keywords: Gibbard-Satterthwaite theorem
MaRDI profile type: Publication
full work available at URL: s00199-002-0285-8
OpenAlex ID: W4245937112
DOI: 10.1007/S00199-002-0285-8
description: scientific article; zbMATH DE number 1983470