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False-Name Manipulation in Weighted Voting Games Is Hard for Probabilistic Polynomial Time

  • Anja Rey
  • Jörg Rothe
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8392)

Abstract

False-name manipulation refers to the question of whether a player in a weighted voting game can increase her power by splitting into several players and distributing her weight among these false identities. Analogously to this splitting problem, the beneficial merging problem asks whether a coalition of players can increase their power in a weighted voting game by merging their weights. Aziz et al. [1] analyze the problem of whether merging or splitting players in weighted voting games is beneficial in terms of the Shapley–Shubik and the normalized Banzhaf index, and so do Rey and Rothe [20] for the probabilistic Banzhaf index. All these results provide merely NP-hardness lower bounds for these problems, leaving the question about their exact complexity open. For the Shapley–Shubik and the probabilistic Banzhaf index, we raise these lower bounds to hardness for PP, “probabilistic polynomial time,” and provide matching upper bounds for beneficial merging and, whenever the new players’ weights are given, also for beneficial splitting, thus resolving previous conjectures in the affirmative. It follows from our results that beneficial merging and splitting for these two power indices cannot be solved in NP, unless the polynomial hierarchy collapses, which is considered highly unlikely.

Keywords

Multiagent System Markov Decision Process Power Index Simple Game Vote Game 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Anja Rey
    • 1
  • Jörg Rothe
    • 1
  1. 1.Institut für InformatikHeinrich-Heine-Universität DüsseldorfDüsseldorfGermany

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