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A generating functions approach for computing the Public Good index efficiently

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  • Michela Chessa

Abstract

In the past years, a combinatorial method based on generating functions was introduced to compute Shapley–Shubik, Banzhaf and other indices for weighted majority games exactly and efficiently. In this paper, taking inspiration from what has already been done, in view of the efficiency of the generating functions method, we define a generating function for computing the Public Good index, maintaining the property of exactness of the resulting algorithm. The main difference with the existing algorithms derives from the fact that the Public Good index takes into account only minimal winning coalitions and counts how many swings of a player involve them. Moreover, we study the computational complexity of the algorithm and we evaluate the Public Good index for the vote share of the Russian Duma in 1995. Copyright Sociedad de Estadística e Investigación Operativa 2014

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  • Michela Chessa, 2014. "A generating functions approach for computing the Public Good index efficiently," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 658-673, July.
    • Handle: RePEc:spr:topjnl:v:22:y:2014:i:2:p:658-673
    DOI: 10.1007/s11750-013-0286-8
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    References listed on IDEAS

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    Cited by:

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    2. Alonso-Meijide, J.M. & Casas-Méndez, B. & Fiestras-Janeiro, M.G., 2015. "Computing Banzhaf–Coleman and Shapley–Shubik power indices with incompatible players," Applied Mathematics and Computation, Elsevier, vol. 252(C), pages 377-387.
    3. Gusev, Vasily V., 2023. "Set-weighted games and their application to the cover problem," European Journal of Operational Research, Elsevier, vol. 305(1), pages 438-450.
    4. Gusev, Vasily V., 2020. "The vertex cover game: Application to transport networks," Omega, Elsevier, vol. 97(C).
    5. Antônio Francisco Neto, 2019. "Generating Functions of Weighted Voting Games, MacMahon’s Partition Analysis, and Clifford Algebras," Mathematics of Operations Research, INFORMS, vol. 44(1), pages 74-101, February.
    6. Vasily V. Gusev, 2021. "Set-weighted games and their application to the cover problem," HSE Working papers WP BRP 247/EC/2021, National Research University Higher School of Economics.

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