Approval voting under dichotomous preferences: a catalogue of characterizations
type: Item
instance of: scholarly article
title: Approval voting under dichotomous preferences: a catalogue of characterizations
author: Florian Brandl
author: Dominik Peters
published in: Journal of Economic Theory
publication date: 2022-11-09T00:00:00Z
review text: The authors give eight characterizations of approval voting. All their results involve the consistency axiom, which requires choices to be consistent across different electorates. In addition, the authors consider strategy-proofness, agreement with majority opinions, independence of cloned alternatives, and invariance under removing inferior alternatives. They prove their results by reducing them to a single base theorem, Theorem 1: approval voting (AV) is the only ballot aggregation function satisfying consistency, disjoint equality and faithfulness. Let \(X\) be a finite set of alternatives. A ballot \(A\) is a non-empty set of (approved) alternatives and let \(\mathcal{A}\) be the set of all ballots. A ballot profile \(P\) is a function which assigns to each ballot \(A\) the number of voters whose ballot is \(A\). The approval score of an alternative \(a\), denoted by \(P[a]\), is the number of voters whose ballot includes \(a\). \(P + A\) denotes the profile resulting from \(P\) by adding one voter with ballot \(A\) and the profile \(P + k A\) is obtained from \(P\) by adding \(k\) voters with ballot \(A\) to \(P\). For a permutation \(\pi\) on \(X\), the profile \(\pi(P)\) has \(P(A)\) voters with ballot \(\pi(A)\) for every ballot \(A\). A ballot aggregation function \(f\) maps each profile \(P\) to a set \(f(P)\) of winning alternatives; typically, \(f(P)\) will be a singleton set. \(f\) is \textit{neutral} iff \(f(\pi(P)) = \pi(f(P))\). \(f\) is \textit{consistent} iff \(f(P + P') = f(P) \cap f(P')\) whenever \(f(P) \cap f(P') \neq \emptyset\). \(f\) is \textit{faithful} iff \(f(A) = A\). \(f\) is \textit{continuous} iff whenever \(f(P) = \{a\}\), there is a natural number \(k\) such that \(f(P' + kP) = \{a\}\). \(f\) satisfies \textit{disjoint equality} iff \(f(A + B) = A \cup B\) whenever \(A \cap B = \emptyset\). And \(f\) satisfies \textit{cancellation} iff \(f(P) = X\) whenever \(P[a] = P[b]\) for all \(a, b \in X\). Examples in Appendix B show that no …
Mathematics Subject Classification ID: 91B12
Mathematics Subject Classification ID: 91B14
zbMATH DE Number: 7614323
zbMATH Keywords: approval voting
zbMATH Keywords: dichotomous preferences
zbMATH Keywords: consistency with variable electorates
zbMATH Keywords: strategyproofness
zbMATH Keywords: Condorcet consistency
zbMATH Keywords: variable agendas
Wikidata QID: Q114160455
MaRDI profile type: Publication
full work available at URL: j.jet.2022.105532
OpenAlex ID: W4293385687
cites work: Q4382651
cites work: Size approval voting
cites work: Non-anonymous ballot aggregation: an axiomatic generalization of approval voting
cites work: A simple characterization of approval voting
cites work: Strongly sincere best responses under approval voting and arbitrary preferences
cites work: Two field experiments on approval voting in Germany
cites work: Independent necessary and sufficient conditions for approval voting
cites work: Random Matching Under Dichotomous Preferences
cites work: Collective choice under dichotomous preferences
cites work: Q3323629
cites work: Set-monotonicity implies Kelly-strategyproofness
cites work: Set-rationalizable choice and self-stability
cites work: Strategyproof social choice when preferences and outcomes may contain ties
cites work: Approval voting without ballot restrictions
cites work: Rational Selection of Decision Functions
cites work: A simple characterization of plurality rule
cites work: Axioms for approval voting: Direct proof
cites work: Q4199792
cites work: The Simple Majority Decision Rule
cites work: Strategy-Proofness and Social Choice Functions without Singlevaluedness
cites work: Consistent approval-based multi-winner rules
cites work: Handbook on approval voting
cites work: A live experiment on approval voting
cites work: Majority rule on \(j\)-rich ballot spaces
cites work: Une caractérisation du vote à la majorité simple
cites work: Pareto efficient combinatorial auctions: dichotomous preferences without quasilinearity
cites work: Weighted approval voting
cites work: Q3661258
cites work: Q3993509
cites work: Concorcet's principle implies the no show paradox
cites work: Axiomatic derivation of scoring rules without the ordering assumption
cites work: Consistency of scoring rules: a reinvestigation of composition-consistency
cites work: Variable-population voting rules
cites work: A characterization result for the plurality rule
cites work: Consequences of reversing preferences
cites work: Scoring rules cannot respect majority in choice and elimination simultaneously
cites work: A characterization result for approval voting with a variable set of alternatives
cites work: Approval voting and fixed electorate with dichotomous preferences
cites work: Social Choice Theory: A Re-Examination
cites work: Characterizing approval voting
cites work: Aggregation of Preferences with Variable Electorate
cites work: Independence of clones as a criterion for voting rules
cites work: Approval voting on dichotomous preferences
cites work: Scoring rules on dichotomous preferences
cites work: Axiomatizations of Approval Voting
cites work: Social Choice Scoring Functions
cites work: A Consistent Extension of Condorcet’s Election Principle
DOI: 10.1016/J.JET.2022.105532
description: scientific article; zbMATH DE number 7614323