Worst Case in Voting and Bargaining

Anna Bogomolnaia (), Ron Holzman () and Herve Moulin
Additional contact information
Anna Bogomolnaia: University of Glasgow and Centre d'Economie de la Sorbonne, https://centredeconomiesorbonne.cnrs.fr
Ron Holzman: Technion-Israel Institute of Technology, https://www.technion.ac.il/en/home-2/

Documents de travail du Centre d'Economie de la Sorbonne from Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne

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)
JEL-codes: D63 D71 (search for similar items in EconPapers)
Pages: 34 pages
Date: 2021-04
References: Add references at CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://mse.univ-paris1.fr/pub/mse/CES2021/21012.pdf (application/pdf)
https://halshs.archives-ouvertes.fr/halshs-03196999
https://arxiv.org/abs/2104.02316

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