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"> 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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Worst Case in Voting and Bargaining

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Abstract
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

Suggested Citation

  • Anna Bogomolnaia & Ron Holzman & Hervé Moulin, 2021. "Worst Case in Voting and Bargaining," Documents de travail du Centre d'Economie de la Sorbonne 21012, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    • Handle: RePEc:mse:cesdoc:21012
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    Cited by:

    1. Margarita Kirneva & Matias Nunez, 2021. "Voting by Simultaneous Vetoes," Working Papers 2021-08, Center for Research in Economics and Statistics.

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    More about this item

    Keywords

    worst case; guarantees; voting by veto; random dictator;
    All these keywords.

    JEL classification:

    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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