Weekly Economics Seminar by Hervé Moulin
March 31 @ 1:30 pm - 2:40 pm
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Title: Worst Case in Voting and Bargaining [link to paper]
Speaker: Hervé Moulin, Professor, University of Glasgow
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 > 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 vetos with one of random dictatorship. If p > n ≥ 3 it is a simplicial complex of dimension d = \ceil((p-1)/d);, that we describe in detail only when d = 1. The dual veto and random dictator guarantees, together with the uniform one, are the building blocks of 2^d simplexes of dimension d in M(n; p). Their vertices are guarantees easy to interpret and implement.