Scoring rules and social choice properties: some characterizations

In many voting systems, voters’ preferences on a set of candidates are represented by linear orderings. In this context, scoring rules are well-known procedures to aggregate the preferences of the voters. Under these rules, each candidate obtains a fixed number of points, s k , each time he/she is r...

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Bibliographic Details
Published in:Theory and decision 2015-03, Vol.78 (3), p.429-450
Main Authors: Llamazares, Bonifacio, Peña, Teresa
Format: Article
Language:English
Subjects:
Aggregates
Axioms
Behavioral/Experimental Economics
Candidates
Decision theory
Economic Theory/Quantitative Economics/Mathematical Methods
Economics
Economics and Finance
Finance
Game Theory
Immunity
Insurance
Management
Mathematical analysis
Meetings
Operations Research/Decision Theory
Pareto efficiency
Pareto optimum
Preferences
Property
Public choice
Ranking systems
Rules and Practice
Scoring
Social and Behav. Sciences
Social Choice
Statistics for Business
Studies
Symmetry
Texts
Voters
Voting
Voting Rules
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Summary:In many voting systems, voters’ preferences on a set of candidates are represented by linear orderings. In this context, scoring rules are well-known procedures to aggregate the preferences of the voters. Under these rules, each candidate obtains a fixed number of points, s k , each time he/she is ranked k th by one voter and the candidates are ordered according to the total number of points they receive. In order to identify the best scoring rule to use in each situation, we need to know which properties are met by each of these procedures. Although some properties have been analyzed extensively, there are other properties that have not been studied for all scoring rules. In this paper, we consider two desirable social choice properties, the Pareto-optimality and the immunity to the absolute loser paradox, and establish characterizations of the scoring rules that satisfy each of these specific axioms. Moreover, we also provide a proof of a result given by Saari and Barney (The Mathematical Intelligencer 25:17–31, 2003 ), where the scoring rules meeting reversal symmetry are characterized. From the results of characterization, we establish some relationships among these properties. Finally, we give a characterization of the scoring rules satisfying the three properties.
ISSN:0040-5833
1573-7187
DOI:10.1007/s11238-014-9429-0