Wost Case in Voting and Bargaining

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Tác giả: Anna bogomolnaia Ron Holzman Herve Moulin

Ngôn ngữ: eng

Ký hiệu phân loại: 302.13 Social choice

Thông tin xuất bản: 2021

Mô tả vật lý:

Bộ sưu tập: Metadata

ID: 166682

 Comment: 33 pagesThe 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 is no less than 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>
 2, we show that the dual veto and random dictator guarantees, together with the uniform one, are the building blocks of 2 to the power d simplices of dimension d in M(n,p), where d is the quotient of p-1 by n. 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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