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Computing power indices for weighted voting games via dynamic programming

Author

Listed:
  • Jochen Staudacher
  • László Á. Kóczy
  • Izabella Stach
  • Jan Filipp
  • Marcus Kramer
  • Till Noffke
  • Linuss Olsson
  • Jonas Pichler
  • Tobias Singer

Abstract

We study the efficient computation of power indices for weighted voting games using the paradigm of dynamic programming. We survey the state-of-the-art algorithms for computing the Banzhaf and Shapley-Shubik indices and point out how these approaches carry over to related power indices. Within a unified framework, we present new efficient algorithms for the Public Good index and a recently proposed power index based on minimal winning coalitions of the smallest size, as well as a very first method for computing the Johnston indices for weighted voting games efficiently. We introduce a software package providing fast C++ implementations of all the power indices mentioned in this article, discuss computing times, as well as storage requirements.

Suggested Citation

  • Jochen Staudacher & László Á. Kóczy & Izabella Stach & Jan Filipp & Marcus Kramer & Till Noffke & Linuss Olsson & Jonas Pichler & Tobias Singer, 2021. "Computing power indices for weighted voting games via dynamic programming," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 31(2), pages 123-145.
    • Handle: RePEc:wut:journl:v:31:y:2021:i:2:p:61-76:id:1576
    DOI: 10.37190/ord210206
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    References listed on IDEAS

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    1. Pattanaik, Prasanta K, 1970. "Sufficient Conditions for the Existence of a Choice Set Under Majority Voting," Econometrica, Econometric Society, vol. 38(1), pages 165-170, January.
    2. Gilboa,Itzhak, 2009. "Theory of Decision under Uncertainty," Cambridge Books, Cambridge University Press, number 9780521517324, October.
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