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Pseudo polynomial size LP formulation for calculating the least core value of weighted voting games

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  • Tanaka, Masato
  • Matsui, Tomomi

Abstract

In this paper, we propose a pseudo polynomial size LP formulation for finding a payoff vector in the least core of a weighted voting game. The numbers of variables and constraints in our formulation are both bounded by O(nW+), where n is the number of players and W+ is the total sum of (integer) voting weights. When we employ our formulation, a commercial LP solver calculates a payoff vector in the least core of practical weighted voting games in a few seconds. We also extend our approach to vector weighted voting games.

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  • Tanaka, Masato & Matsui, Tomomi, 2022. "Pseudo polynomial size LP formulation for calculating the least core value of weighted voting games," Mathematical Social Sciences, Elsevier, vol. 115(C), pages 47-51.
    • Handle: RePEc:eee:matsoc:v:115:y:2022:i:c:p:47-51
    DOI: 10.1016/j.mathsocsci.2021.12.002
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    References listed on IDEAS

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    1. Sascha Kurz, 2012. "On minimum sum representations for weighted voting games," Annals of Operations Research, Springer, vol. 196(1), pages 361-369, July.
    2. Paola Cappanera & Maria Paola Scaparra, 2011. "Optimal Allocation of Protective Resources in Shortest-Path Networks," Transportation Science, INFORMS, vol. 45(1), pages 64-80, February.
    3. Robert G. Bland & Donald Goldfarb & Michael J. Todd, 1981. "Feature Article—The Ellipsoid Method: A Survey," Operations Research, INFORMS, vol. 29(6), pages 1039-1091, December.
    4. Moshé Machover & Dan S. Felsenthal, 2001. "The Treaty of Nice and qualified majority voting," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(3), pages 431-464.
    5. Prasad, K & Kelly, J S, 1990. "NP-Completeness of Some Problems Concerning Voting Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 19(1), pages 1-9.
    6. Shapley, L. S. & Shubik, Martin, 1954. "A Method for Evaluating the Distribution of Power in a Committee System," American Political Science Review, Cambridge University Press, vol. 48(3), pages 787-792, September.
    7. Bilbao, J. M. & Fernandez, J. R. & Jimenez, N. & Lopez, J. J., 2002. "Voting power in the European Union enlargement," European Journal of Operational Research, Elsevier, vol. 143(1), pages 181-196, November.
    8. Kurz, Sascha & Napel, Stefan & Nohn, Andreas, 2014. "The nucleolus of large majority games," Economics Letters, Elsevier, vol. 123(2), pages 139-143.
    9. Josep Freixas & Xavier Molinero, 2009. "On the existence of a minimum integer representation for weighted voting systems," Annals of Operations Research, Springer, vol. 166(1), pages 243-260, February.
    10. SCHMEIDLER, David, 1969. "The nucleolus of a characteristic function game," LIDAM Reprints CORE 44, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    11. M. Maschler & B. Peleg & L. S. Shapley, 1979. "Geometric Properties of the Kernel, Nucleolus, and Related Solution Concepts," Mathematics of Operations Research, INFORMS, vol. 4(4), pages 303-338, November.
    12. Xiaotie Deng & Christos H. Papadimitriou, 1994. "On the Complexity of Cooperative Solution Concepts," Mathematics of Operations Research, INFORMS, vol. 19(2), pages 257-266, May.
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