Power structure and cardinality restrictions for Paretian social choice rules
type: Item
instance of: scholarly article
title: Power structure and cardinality restrictions for Paretian social choice rules
zbMATH Open document ID: 0549.90003
DOI: 10.1007/BF00452882
author: Edward W. Packel
published in: Social Choice and Welfare
publication date: 1984-01-01T00:00:00Z
review text: Let f be a multiple-valued Paretian social choice rule for n voters and an outcome set X. The preventing sets for f are shown to form an acyclic majority when \(| X| <n\), a prefilter when \(| X|\geq n\), and a filter when f also satisfies a binary independence condition. These results are then shown to yield inequalities relating \(| X|\), n, and certain preventing sets. In particular, if every coalition of q voters constitutes a preventing set, then \(| X|\leq [n-1/n-q]\). Other inequalities are obtained if strong equilibria are present for every preference profile.
Mathematics Subject Classification ID: 91B14
zbMATH DE Number: 3876858
zbMATH Keywords: multiple-valued Paretian social choice rule
zbMATH Keywords: preventing sets
zbMATH Keywords: acyclic majority
zbMATH Keywords: prefilter
zbMATH Keywords: strong equilibria
MaRDI profile type: Publication
cites work: The Implementation of Social Choice Rules: Some General Results on Incentive Compatibility
cites work: On Nicely Consistent Voting Systems
cites work: Manipulation of Voting Schemes: A General Result
cites work: Construction of Outcome Functions Guaranteeing Existence and Pareto Optimality of Nash Equilibria
cites work: Q3901249
cites work: The vetoers in a simple game with ordinal preferences
cites work: Strategic equilibria and decisive set structures for social choice mechanisms
cites work: Consistent Voting Systems
cites work: Strategy-proofness and Arrow's conditions: existence and correspondence theorems for voting procedures and social welfare functions
full work available at URL: https://doi.org/10.1007/bf00452882
OpenAlex ID: W2246577453
description: scientific article; zbMATH DE number 3876858