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Generating functions for computing power indices efficiently

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  • J. Bilbao
  • J. Fernández
  • A. Losada
  • J. López

Abstract

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  • J. Bilbao & J. Fernández & A. Losada & J. López, 2000. "Generating functions for computing power indices efficiently," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 8(2), pages 191-213, December.
    • Handle: RePEc:spr:topjnl:v:8:y:2000:i:2:p:191-213
    DOI: 10.1007/BF02628555
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    References listed on IDEAS

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    1. Dan S. Felsenthal & Moshé Machover, 1998. "The Measurement of Voting Power," Books, Edward Elgar Publishing, number 1489.
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    Cited by:

    1. Birkmeier Olga & Käufl Andreas & Pukelsheim Friedrich, 2011. "Abstentions in the German Bundesrat and ternary decision rules in weighted voting systems," Statistics & Risk Modeling, De Gruyter, vol. 28(1), pages 1-16, March.
    2. M. Musegaas & P. E. M. Borm & M. Quant, 2018. "Three-valued simple games," Theory and Decision, Springer, vol. 85(2), pages 201-224, August.
    3. Roberto Lucchetti & Paola Radrizzani & Emanuele Munarini, 2011. "A new family of regular semivalues and applications," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(4), pages 655-675, November.
    4. Bolus, Stefan, 2011. "Power indices of simple games and vector-weighted majority games by means of binary decision diagrams," European Journal of Operational Research, Elsevier, vol. 210(2), pages 258-272, April.
    5. 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.
    6. Phuoc Hoang Le & Tri-Dung Nguyen & Tolga Bektaş, 2020. "Efficient computation of the Shapley value for large-scale linear production games," Annals of Operations Research, Springer, vol. 287(2), pages 761-781, April.
    7. Dennis Leech, 2003. "Computing Power Indices for Large Voting Games," Management Science, INFORMS, vol. 49(6), pages 831-837, June.
    8. Matthew Gould & Matthew D. Rablen, 2017. "Reform of the United Nations Security Council: equity and efficiency," Public Choice, Springer, vol. 173(1), pages 145-168, October.
    9. Antônio Francisco Neto & Carolina Rodrigues Fonseca, 2019. "An approach via generating functions to compute power indices of multiple weighted voting games with incompatible players," Annals of Operations Research, Springer, vol. 279(1), pages 221-249, August.
    10. Serguei Kaniovski & Sascha Kurz, 2018. "Representation-compatible power indices," Annals of Operations Research, Springer, vol. 264(1), pages 235-265, May.
    11. 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.
    12. Wilms, Ingo, 2020. "Dynamic programming algorithms for computing power indices in weighted multi-tier games," Mathematical Social Sciences, Elsevier, vol. 108(C), pages 175-192.
    13. Konstantin Avrachenkov & Laura Cottatellucci & Lorenzo Maggi, 2014. "Confidence Intervals for the Shapley–Shubik Power Index in Markovian Games," Dynamic Games and Applications, Springer, vol. 4(1), pages 10-31, March.
    14. Gianfranco Gambarelli & Angelo Uristani, 2009. "Multicameral voting cohesion games," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 17(4), pages 433-460, December.
    15. Martí Jané Ballarín, 2023. "The complexity of power indices in voting games with incompatible players," UB School of Economics Working Papers 2023/441, University of Barcelona School of Economics.
    16. Yuto Ushioda & Masato Tanaka & Tomomi Matsui, 2022. "Monte Carlo Methods for the Shapley–Shubik Power Index," Games, MDPI, vol. 13(3), pages 1-14, June.
    17. Hang Luo & Lize Yang & Kourosh Houshmand, 2021. "Power Structure Dynamics in Growing Multilateral Development Banks: The Case of the Asian Infrastructure Investment Bank," Global Policy, London School of Economics and Political Science, vol. 12(1), pages 24-39, February.
    18. Benati, Stefano & Rizzi, Romeo & Tovey, Craig, 2015. "The complexity of power indexes with graph restricted coalitions," Mathematical Social Sciences, Elsevier, vol. 76(C), pages 53-63.
    19. Benati, Stefano & López-Blázquez, Fernando & Puerto, Justo, 2019. "A stochastic approach to approximate values in cooperative games," European Journal of Operational Research, Elsevier, vol. 279(1), pages 93-106.
    20. Stefano Benati & Giuseppe Vittucci Marzetti, 2021. "Voting power on a graph connected political space with an application to decision-making in the Council of the European Union," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 57(4), pages 733-761, November.
    21. 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.
    22. Somdeb Lahiri, 2021. "Pattanaik's axioms and the existence of winners preferred with probability at least half," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 31(2), pages 109-122.
    23. de Moura, Gustavo Nikolaus Pinto & Legey, Luiz Fernando Loureiro & Howells, Mark, 2018. "A Brazilian perspective of power systems integration using OSeMOSYS SAMBA – South America Model Base – and the bargaining power of neighbouring countries: A cooperative games approach," Energy Policy, Elsevier, vol. 115(C), pages 470-485.
    24. Matthew Gould & Matthew D. Rablen, 2019. "Are World Leaders Loss Averse?," CESifo Working Paper Series 7763, CESifo.

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