The Complexity of Power-Index Comparison

  • Piotr Faliszewski
  • Lane A. Hemaspaandra
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5034)


We study the complexity of the following problem: Given two weighted voting games G′ and G′′ that each contain a player p, in which of these games is p’s power index value higher? We study this problem with respect to both the Shapley-Shubik power index [16] and the Banzhaf power index [3,6]. Our main result is that for both of these power indices the problem is complete for probabilistic polynomial time (i.e., is PP-complete). We apply our results to partially resolve some recently proposed problems regarding the complexity of weighted voting games. We also show that, unlike the Banzhaf power index, the Shapley-Shubik power index is not #P-parsimonious-complete. This finding sets a hard limit on the possible strengthenings of a result of Deng and Papadimitriou [5], who showed that the Shapley-Shubik power index is #P-metric-complete.


Weighted voting games power indices computational complexity 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Piotr Faliszewski
    • 1
  • Lane A. Hemaspaandra
    • 1
  1. 1.Department of Computer ScienceUniversity of RochesterRochester 

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