• A
  • A
  • A
  • ABC
  • ABC
  • ABC
  • А
  • А
  • А
  • А
  • А
Regular version of the site

Working paper

Worst Case in Voting and Bargaining

Bogomolnaia A., Moulin H., Holzman R.
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 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.