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Weighted and roughly weighted simple games

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  • Gvozdeva, Tatiana
  • Slinko, Arkadii

Abstract

In this paper we give necessary and sufficient conditions for a simple game to have rough weights. We define two functions f(n) and g(n) that measure the deviation of a simple game from a weighted majority game and roughly weighted majority game, respectively. We formulate known results in terms of lower and upper bounds for these functions and improve those bounds. We also investigate rough weightedness of simple games with a small number of players.

Suggested Citation

  • Gvozdeva, Tatiana & Slinko, Arkadii, 2011. "Weighted and roughly weighted simple games," Mathematical Social Sciences, Elsevier, vol. 61(1), pages 20-30, January.
    • Handle: RePEc:eee:matsoc:v:61:y:2011:i:1:p:20-30
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    References listed on IDEAS

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    1. Steven J. Brams & William V. Gehrlein & Fred S. Roberts (ed.), 2009. "The Mathematics of Preference, Choice and Order," Studies in Choice and Welfare, Springer, number 978-3-540-79128-7, December.
    2. Arkadii Slinko, 2009. "Additive Representability of Finite Measurement Structures," Studies in Choice and Welfare, in: Steven J. Brams & William V. Gehrlein & Fred S. Roberts (ed.), The Mathematics of Preference, Choice and Order, pages 113-133, Springer.
    3. Carreras, Francesc & Freixas, Josep, 1996. "Complete simple games," Mathematical Social Sciences, Elsevier, vol. 32(2), pages 139-155, October.
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    Cited by:

    1. René Brink & Dinko Dimitrov & Agnieszka Rusinowska, 2021. "Winning coalitions in plurality voting democracies," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 56(3), pages 509-530, April.
    2. Tatiana Gvozdeva & Lane Hemaspaandra & Arkadii Slinko, 2013. "Three hierarchies of simple games parameterized by “resource” parameters," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(1), pages 1-17, February.
    3. Josep Freixas & Sascha Kurz, 2014. "On $${\alpha }$$ α -roughly weighted games," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(3), pages 659-692, August.
    4. Houy, Nicolas & Zwicker, William S., 2014. "The geometry of voting power: Weighted voting and hyper-ellipsoids," Games and Economic Behavior, Elsevier, vol. 84(C), pages 7-16.
    5. Josep Freixas & Sascha Kurz, 2014. "Enumeration of weighted games with minimum and an analysis of voting power for bipartite complete games with minimum," Annals of Operations Research, Springer, vol. 222(1), pages 317-339, November.
    6. Freixas, Josep & Kurz, Sascha, 2013. "The golden number and Fibonacci sequences in the design of voting structures," European Journal of Operational Research, Elsevier, vol. 226(2), pages 246-257.
    7. Josep Freixas & Marc Freixas & Sascha Kurz, 2017. "On the characterization of weighted simple games," Theory and Decision, Springer, vol. 83(4), pages 469-498, December.
    8. Akihiro Kawana & Tomomi Matsui, 2022. "Trading transforms of non-weighted simple games and integer weights of weighted simple games," Theory and Decision, Springer, vol. 93(1), pages 131-150, July.
    9. Gvozdeva, Tatiana & Hameed, Ali & Slinko, Arkadii, 2013. "Weightedness and structural characterization of hierarchical simple games," Mathematical Social Sciences, Elsevier, vol. 65(3), pages 181-189.
    10. Ali Hameed & Arkadii Slinko, 2015. "Roughly weighted hierarchical simple games," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(2), pages 295-319, May.

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