Generalized average rules as stable Nash mechanisms to implement generalized median rules

We characterize the set of all obviously strategy-proof and onto social choice functions on the domain of single-peaked preferences. Since obvious strategyproofness implies strategy-proofness, and the set of strategy-proof and onto social choice functions on this domain coincides with the class of generalized median voter schemes, we focus on this class. We identify a condition on generalized median voter schemes for which the following characterization holds. A generalized median voter scheme is obviously strategy-proof if and only if it satis…es the increasing intersection property. Our proof is constructive; for each generalized median voter scheme that satis…es the increasing intersection property we de…ne an extensive game form that implements it in obviously dominant strategies.

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“…Observe that X 1 and/or Y t could be empty. 21 Since the proto-dictatorship OSP-implements f and C x = C x ; it can be checked that C m…”

Section: Proof Of Theoremmentioning

confidence: 99%

On obvious strategy-proofness and single-peakedness

Arribillaga

Massó

Neme

2020

Journal of Economic Theory

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“…In other words, the device used to determine this index is the trimmed mean rule. Theorists have mostly focused on the pure mean rule (without trimming) and their conclusion over its properties is qualified (see Renault and Trannoy [2005] and Yamamura and Kawasaki [2013] for theoretical works on this subject and Marchese and Montefiori [2011] and Block et al [2014] for experimental ones). In environments with a large number of voters, this rule seems to be a natural candidate as it is the unique one satisfying a weakening of strategy-proofness (see Ehlers et al [2004]).…”

Section: Relevant Literaturementioning

confidence: 99%

“…Yet, it often lacks general results, while succeeding in tailoring interesting mechanisms for particular situations. In this literature, the most closely related contributions are the ones by Yamamura and Kawasaki [2013] and Gershkov et al [2015] and the one by Saijo et al [2007]. Yamamura and Kawasaki [2013] proves how to implement GMRs through a class of simple direct mechanisms: the average rules.…”

Section: Relevant Literaturementioning

confidence: 99%

“…In this literature, the most closely related contributions are the ones by Yamamura and Kawasaki [2013] and Gershkov et al [2015] and the one by Saijo et al [2007]. Yamamura and Kawasaki [2013] proves how to implement GMRs through a class of simple direct mechanisms: the average rules. As they show, the agents tend to adopt an extremist behavior (either 0 or 1) in equilibrium.…”

Section: Relevant Literaturementioning

confidence: 99%

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Unanimous Implementation: A Case for Approval Mechanisms

Núñez

Xefteris

2016

SSRN Journal

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We design the class of (indirect) Approval mechanisms which allow the players' strategies to coincide with the subsets of the outcome space. By focusing on the single-peaked domain, we prove that: a) Each of these mechanisms is characterized by a unique equilibrium outcome, and b) for almost every implementable welfare optimum (outcome of a social choice rule), including the Condorcet winner alternative, there exists an Approval mechanism that unanimously implements it. That is, Approval mechanisms help a society achieve every feasible welfare goal, and, perhaps more importantly, they promote social coherence: The implemented outcome is approved by everyone.

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“…4 So how do we Nash-implement GMRs in a simple manner? Yamamura and Kawasaki [2013] propose the class of averaging mechanisms. Each player announces an alternative and a monotonic transformation of the average alternative is implemented.…”

Section: Introductionmentioning

confidence: 99%

Implementation via approval mechanisms

Núñez

Xefteris

2017

Journal of Economic Theory

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We focus on the single-peaked domain and study the class of Generalized Approval Mechanisms (GAMs): First, players simultaneously select subsets of the outcome space and scores are assigned to each alternative; and, then, a given quantile of the induced score distribution is implemented. Our main finding is that essentially for every Nash-implementable welfare optimum-including the Condorcet winner alternative-there exists a GAM that Nashimplements it. Importantly, the GAM that Nash-implements the Condorcet winner alternative is the first simple simultaneous game with this feature in the literature.

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Generalized average rules as stable Nash mechanisms to implement generalized median rules

Cited by 20 publications

References 30 publications

On obvious strategy-proofness and single-peakedness

On obvious strategy-proofness and single-peakedness

Unanimous Implementation: A Case for Approval Mechanisms

Implementation via approval mechanisms

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