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Autre publication scientifique Documents de travail du Centre d'Économie de la Sorbonne Année : 2021

Worst Case in Voting and Bargaining

Résumé

The guarantee of an anonymous mechanism is the worst case welfare an agent can secure against unanimously adversarial others. How high can such a guarantee be, and what type of mechanism achieves it?. We address the worst case design question in the n-person probabilistic voting/bargaining model with p deterministic outcomes. If n superior or equal to p the uniform lottery is the only maximal (unimprovable) guarantee; there are many more if p>n, in particular the ones inspired by the random dictator mechanism and by voting by veto. If n=2 the maximal set M(n,p) is a simple polytope where each vertex combines a round of vetoes with one of random dictatorship. For p>n superior or egal to 3, writing d=[((p-1)/n)], we show that the duak veto and random dictator guarantees, together with the uniform one, are the building blocks of 2^{d} simplices of dimension d in M(n,p). Their vertices are guarantees easy to interpret and implement. The set M(n,p) may contain other guarantees as well; what we can say in full generality is that it is a finite union of polytopes, all sharing the uniform guarantee.
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Dates et versions

halshs-03196999, version 1 (13-04-2021)

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  • HAL Id : halshs-03196999 , version 1

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Anna Bogomolnaia, Ron Holzman, Hervé Moulin. Worst Case in Voting and Bargaining. 2021. ⟨halshs-03196999⟩
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Dernière date de mise à jour le 05/05/2024
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