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Computing power indices for weighted voting games via dynamic programming

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STAUDACHER J., KÓCZY L. Á., STACH I., FILIPP J., KRAMER M., NOFFKE T., OLSSON L., PICHLER J., SINGER T.
Operations Research and Decisions
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2021
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vol. 31
|
issue 2
123-145
EN
We study the efficient computation of power indices for weighted voting games using the para- digm 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.
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