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Worst Case in Voting and Bargaining

Anna Bogomolnaia (), Ron Holzman () and Herve Moulin ()
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Anna Bogomolnaia: CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, University of Glasgow, HSE St Petersburg - Higher School of Economics - St Petersburg
Ron Holzman: Technion - Israel Institute of Technology [Haifa]

Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) from HAL

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.

Keywords: worst case; guarantees; voting by veto; random dictator (search for similar items in EconPapers)
Date: 2021-04
Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-03196999
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Published in 2021

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Working Paper: Worst Case in Voting and Bargaining (2021) Downloads
Working Paper: Worst Case in Voting and Bargaining (2021) Downloads
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