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International Conference on Algorithmic Applications in Management

AAIM 2008: Algorithmic Aspects in Information and Management pp 177–187Cite as

The Complexity of Power-Index Comparison

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Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 5034))

Abstract

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.

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Authors and Affiliations

  1. Department of Computer Science, University of Rochester, Rochester, NY 14627,  

    Piotr Faliszewski & Lane A. Hemaspaandra

Authors
  1. Piotr Faliszewski
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  2. Lane A. Hemaspaandra
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Rudolf Fleischer Jinhui Xu

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Faliszewski, P., Hemaspaandra, L.A. (2008). The Complexity of Power-Index Comparison. In: Fleischer, R., Xu, J. (eds) Algorithmic Aspects in Information and Management. AAIM 2008. Lecture Notes in Computer Science, vol 5034. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-68880-8_18

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  • DOI: https://doi.org/10.1007/978-3-540-68880-8_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-68865-5

  • Online ISBN: 978-3-540-68880-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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