The Inverse Shapley value problem

Anindya De, Ilias Diakonikolas, Rocco A. Servedio

Research output: Contribution to journalArticlepeer-review

Abstract

For f a weighted voting scheme used by n voters to choose between two candidates, the n Shapley–Shubik Indices (or Shapley values) of f measure how much control each voter can exert over the overall outcome. The Inverse Shapley Value Problem is the problem of designing a weighted voting scheme which (approximately) achieves a desired input vector of values for the Shapley–Shubik indices. We give the first efficient algorithm with provable guarantees for the Inverse Shapley Value Problem. For any constant ϵ>0 our algorithm runs in fixed poly(n) time and satisfies the following: given as input a vector of desired Shapley values, if any “reasonable” weighted voting scheme (roughly, one in which the threshold is not too skewed) approximately matches the desired vector of values, then our algorithm outputs a weighted voting scheme that achieves this vector of Shapley values to within error ϵ.
Original languageEnglish
Article number26
Pages (from-to)122-147
Number of pages26
JournalGames and Economic Behavior
Volume105
Early online date21 Jul 2017
DOIs
Publication statusPublished - Sep 2017

Keywords

  • Shapley values
  • Weighted voting games
  • Algorithms
  • Fourier Analysis

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