A unified approach to strategy-proofness for single-peaked preferences

Weymark, John A.

doi:10.1007/s13209-011-0064-5

Cited by 25 publications

(18 citation statements)

References 20 publications

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“…Corollary 4.1 (Moulin (1980), Weymark (2011)). Let S i be the maximal set of single-peaked preferences for all i ∈ N. Then, an SCF f : S N → X is unanimous and strategy-proof if and only if it is a min-max rule.…”

Section: X 2 X 2 X 2 X 2 X 3 X 3 X 3 X 3 X 4 X 4 X 5 X 2 X 1 X 3 mentioning

confidence: 95%

“…The study of single-peaked domains dates back to Black (1948), where it is shown that the pairwise majority rule is strategy-proof on such domains. Later, Moulin (1980) and Weymark (2011) characterize the unanimous and strategy-proof SCFs on these domains. 1,2 However, their characterization rests upon the assumption that the set of admissible preferences of each agent in the society is the maximal single-peaked domain, i.e., it contains all single-peaked preferences with respect to a given prior order over the alternatives.…”

Section: Motivation and Contributionmentioning

confidence: 99%

“…The unanimous and strategy-proof SCFs on the maximal single-peaked domain are known as min-max rules (Moulin (1980), Weymark (2011)). Min-max rules are quite popular for their desirable properties like tops-onlyness, Pareto property, and anonymity (for a subclass of min-max rules called median rules).…”

Section: Motivation and Contributionmentioning

confidence: 99%

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On single-peaked domains and min–max rules

Achuthankutty

Roy

2018

Soc Choice Welf

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We consider social choice problems where different agents can have different sets of admissible single-peaked preferences. We show every unanimous and strategy-proof social choice function on such domains satisfies Pareto property and tops-onlyness. Further, we characterize all domains on which (i) every unanimous and strategy-proof social choice function is a min-max rule, and (ii) every min-max rule is strategy-proof. As an application of our result, we obtain a characterization of the unanimous and strategy-proof social choice functions on maximal single-peaked domains (Moulin (1980), Weymark (2011)), minimally rich single-peaked domains (Peters et al. (2014)), maximal regular single-crossing domains (Saporiti (2009), Saporiti (2014)), and distance based single-peaked domains.

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Section: X 2 X 2 X 2 X 2 X 3 X 3 X 3 X 3 X 4 X 4 X 5 X 2 X 1 X 3 mentioning

confidence: 95%

Section: Motivation and Contributionmentioning

confidence: 99%

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On single-peaked domains and min–max rules

Achuthankutty

Roy

2018

Soc Choice Welf

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“…5 Moulin (1980), Barberà et al (1993) and Weymark (2011) characterize the unanimous and strategy-proof SCFs on the single-peaked domains as min-max rules. Peremans and Storcken (1999) and Manjunath (2014) characterize the unanimous and strategy-proof SCFs on the single-dipped domains as voting by extended committees.…”

Section: Our Contributionmentioning

confidence: 99%

Dictatorship on top-circular domains

Achuthankutty

Roy

2018

Theory Decis

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We consider domains with a natural property called top-circularity. We show that if such a domain satisfies either the maximal conflict property or the weak conflict property, then it is dictatorial. We obtain the result in Sato (2010) as a corollary. Further, it follows from our results that the union of a top-connected single-peaked domain and a top-connected single-dipped domain is dictatorial.

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“…Though Lemmas 3.12 and 3.13 use same techniques used in[Moulin, 1980] and[Weymark, 2011], we present them here for the sake of completeness.…”

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confidence: 99%

Social choice: locating public facilities & voting in a large electorate

Chatterjee¹

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A unified approach to strategy-proofness for single-peaked preferences

Cited by 25 publications

References 20 publications

On single-peaked domains and min–max rules

On single-peaked domains and min–max rules

Dictatorship on top-circular domains

Social choice: locating public facilities & voting in a large electorate

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