On domains that admit well-behaved strategy-proof social choice functions

Chatterji, Shurojit; Sanver, M. Remzi; Sen, Arunava

doi:10.1016/j.jet.2012.10.005

Cited by 25 publications

(44 citation statements)

References 23 publications

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“…For instance, the existence of non-dictatorial Arrovian aggregators and/or strategy-proof social choice functions can be demonstrated under much weaker domain restrictions (Kalai and Muller [1977]). Also in this context, richness and/or connectedness assumptions have frequently been imposed, and variants of the single-peakedness condition have been found to play an important role in the derivation of possibility results (Nehring and Puppe [2007], Chatterji et al [2013], Chatterji and Massó [2015]). In a recent paper, Chatterji et al [2016] have characterized a weaker notion of single-peakedness ('single-peakedness with respect to a tree') using strategy-proofness and other conditions imposed on random social choice functions.…”

Section: Resultsmentioning

confidence: 99%

The single-peaked domain revisited: A simple global characterization

Puppe

2018

Journal of Economic Theory

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for particularly helpful comments.Abstract It is proved that, among all restricted preference domains that guarantee consistency (i.e. transitivity) of pairwise majority voting, the single-peaked domain is the only minimally rich and connected domain that contains two completely reversed strict preference orders. It is argued that this result explains the predominant role of single-peakedness as a domain restriction in models of political economy and elsewhere. The main result has a number of corollaries, among them a dual characterization of the single-dipped domain; it also implies that a single-crossing ('order-restricted') domain can be minimally rich only if it is a subdomain of a single-peaked domain. The conclusions are robust as the results apply both to domains of strict and of weak preference orders, respectively. JEL Classification D71, C72

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Section: Resultsmentioning

confidence: 99%

The single-peaked domain revisited: A simple global characterization

Puppe

2018

Journal of Economic Theory

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“…Given a strategy‐proof, tops‐only, and anonymous SCF

g : {scriptD}^{n} \to A

where n is a positive even integer, we start by stating the following fact that appears as proposition in Chatterji et al. (). Fact Let

scriptD

be an arbitrary domain and let n be a positive even integer.…”

Section: Resultsmentioning

confidence: 99%

“…More recently, work by Nehring and Puppe (, , ) and Chatterji et al. () provides formulations of such a converse statement. Our article complements these approaches and is closely related to the approach of these papers in that our axioms on the SCF are similar.…”

Section: Introductionmentioning

confidence: 98%

“…The richness condition in Chatterji et al. () is specified in terms of alternatives that appear as the first‐ and second‐ranked alternatives in different preference orderings that make it specific to a model with finitely many alternatives with strict preferences and also exclude the consideration of preferences commonly employed in the study of multidimensional models. Our formulation is more permissive in that we impose no finiteness requirement on the set of alternatives and, provided the top‐ranked alternative is unique, we admit indifferences.…”

Section: Introductionmentioning

confidence: 99%

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On Strategy‐proofness and the Salience of Single‐peakedness

Chatterji

Massó

2018

Int Economic Review

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We consider strategy‐proof rules operating on a rich domain of preference profiles. We show that if the rule satisfies in addition tops‐onlyness, anonymity, and unanimity, then the preferences in the domain have to satisfy a variant of single‐peakedness (referred to as semilattice single‐peakedness). We do so by deriving from the rule an endogenous partial order (a semilattice) from which the concept of a semilattice single‐peaked preference can be defined. We also provide a converse of this main finding. Finally, we show how well‐known restricted domains under which nontrivial strategy‐proof rules are admissible are semilattice single‐peaked domains.

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“…Our approach here is to strengthen the notion of connectedness of alternatives along the lines initiated in Chatterji et al (2010).…”

Section: Strongly Linked Domains With Condition Tsmentioning

confidence: 99%

Random dictatorship domains

Chatterji¹,

Sen²,

Zeng³

2014

Games and Economic Behavior

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A domain of preference orderings is a random dictatorship domain if every strategyproof random social choice function satisfying unanimity defined on the domain, is a random dictatorship. Gibbard (1977) showed that the universal domain is a random dictatorship domain. We investigate the relationship between dictatorial and random dictatorship domains. We show that there exist dictatorial domains that are not random dictatorship domains. We provide stronger versions of the linked domain condition (introduced in Aswal et al. (2003)) that guarantee that a domain is a random dictatorship domain. A key step in these arguments that is of independent interest, is a ramification result that shows that under certain assumptions, a domain that is a random dictatorship domain for two voters is also a random dictatorship domain for an arbitrary number of voters.

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On domains that admit well-behaved strategy-proof social choice functions

Cited by 25 publications

References 23 publications

The single-peaked domain revisited: A simple global characterization

The single-peaked domain revisited: A simple global characterization

On Strategy‐proofness and the Salience of Single‐peakedness

Random dictatorship domains

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