Multi-valued strategy-proof social choice rules

Ching, Stephen; Zhou, Lin

doi:10.1007/s003550100134

Cited by 71 publications

(58 citation statements)

References 13 publications

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“…We impose two consistency conditions on the family fK ,N K ⊆K,N ⊆N that 6 We do not consider the empty set, because we want to study exclusively situations where some decision has to be taken. Moreover, there are two technical reasons for excluding the empty set: First, since we are interested in strategic voting, we have to make assumptions on how an individual orders subsets of K. Yet, if Di ∈ D is such that G(Di) = ∅ and B(Di) = ∅, then it is not obvious how an individual orders the empty set versus some non-empty subsets of K. For example, if x ∈ G(Di) and y ∈ B(Di), then it is ambiguous whether i prefers the empty set or {x, y}.…”

Section: Notation and Definitionsmentioning

confidence: 99%

“…2 Finally, 1 Among others, further work on set-valued social choice functions is due to Duggan and Schwartz [7], Barberà et. al [1], and Ching and Zhou [6]. 2 Property α states that if one compares two social choice correspondences differing from each other in such a way that the considered set of alternatives in the second problem is a we define a social choice rule to be a family of set-valued social choice functions that is consistent in alternatives and individuals, and therefore, the question we deal with is which social choice rule satisfies a set of desirable properties.…”

Section: Introductionmentioning

confidence: 99%

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Approval Voting on Dichotomous Preferences

Vorsatz

2006

Soc Choice Welfare

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The aim of this paper is to find normative foundations of Approval Voting. In order to show that Approval Voting is the only social choice function that satisfies anonymity, neutrality, strategy-proofness and strict monotonicity we rely on an intermediate result which relates strategy-proofness of a social choice function to the properties of Independence of Irrelevant Alternatives and monotonicity of the corresponding social welfare function. Afterwards we characterize Approval Voting by means of strict symmetry, neutrality and strict monotonicity and relate this result to May's Theorem [11]. Finally, we show that it is possible to substitute the property of strict monotonicity by the one efficiency of in the second characterization.

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Section: Notation and Definitionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Approval Voting on Dichotomous Preferences

Vorsatz

2006

Soc Choice Welfare

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“…Two papers of particular interest are Duggan and Schwartz [8] and Ching and Zhou [7]. We discuss each in turn.…”

Section: Social Choice Correspondencesmentioning

confidence: 99%

“…Hence, their result``almost'' 15 follows from ours. A paper closely related to ours is Benoit [7]. The paper considers social choice rules which, like our social choice functions, map profiles of preferences over sets of basic alternatives to these sets themselves.…”

Section: Social Choice Correspondencesmentioning

confidence: 99%

Strategy-proof Social Choice Correspondences

Barberà¹,

Dutta²,

Sen³

2001

Journal of Economic Theory

104

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We study the possibilities of constructing strategy-proof rules that choose sets of alternatives as a function of agents' preferences over such sets. We consider two restrictions on the domain of individual preferences over sets. Assuming that all singletons are in the range of the rule, we show that only dictatorial rules can be strategy-proof on the larger domain. The smaller domain also allows for rules which select the set of best elements of two fixed agents. Journal of Economic Literature Classification Number: D71.

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“…In contrast to the traditional setup in social choice theory, which typically only involves ordinal preferences, his result relies on the axioms of von Neumann and Morgenstern [36] (or an equivalent set of axioms) in order to compare lotteries over alternatives. The gap between Gibbard and Satterthwaite's theorem for resolute SCFs and Gibbard's theorem for decision schemes has been filled by a number of impossibility results for irresolute SCFs with varying underlying notions of how to compare sets of alternatives with each other (e.g., [15,1,2,22,10,5,8,28,35]), many of which are surveyed by Taylor [34] and Barberà [4].…”

Section: Introductionmentioning

confidence: 99%

Necessary and sufficient conditions for the strategyproofness of irresolute social choice functions

Brandt

Brill

2011

Proceedings of the 13th Conference on Theoretical Aspects of Rationality and Knowledge

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While the Gibbard-Satterthwaite theorem states that every non-dictatorial and resolute, i.e., single-valued, social choice function is manipulable, it was recently shown that a number of appealing irresolute Condorcet extensions are strategyproof according to Kelly's preference extension. In this paper, we study whether these results carry over to stronger preference extensions due to Fishburn and Gärden-fors. For both preference extensions, we provide sufficient conditions for strategyproofness and identify social choice functions that satisfy these conditions, answering a question by Gärdenfors [15] in the affirmative. We also show that some more discriminatory social choice functions fail to satisfy necessary conditions for strategyproofness.

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Multi-valued strategy-proof social choice rules

Cited by 71 publications

References 13 publications

Approval Voting on Dichotomous Preferences

Approval Voting on Dichotomous Preferences

Strategy-proof Social Choice Correspondences

Necessary and sufficient conditions for the strategyproofness of irresolute social choice functions

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