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A relation-algebraic approach to simple games

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  • Berghammer, Rudolf
  • Bolus, Stefan
  • Rusinowska, Agnieszka
  • de Swart, Harrie

Abstract

Simple games are a powerful tool to analyze decision-making and coalition formation in social and political life. In this paper, we present relation-algebraic models of simple games and develop relational specifications for solving some basic problems of them. In particular, we test certain fundamental properties of simple games and compute specific players and coalitions. We also apply relation algebra to determine power indices. This leads to relation-algebraic specifications, which can be evaluated with the help of the BDD-based tool Rel View after a simple translation into the tool's programming language. In order to demonstrate the visualization facilities of Rel View we consider an example of the Catalonian Parliament after the 2003 election.

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Bibliographic Info

Article provided by Elsevier in its journal European Journal of Operational Research.

Volume (Year): 210 (2011)
Issue (Month): 1 (April)
Pages: 68-80

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Handle: RePEc:eee:ejores:v:210:y:2011:i:1:p:68-80

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Web page: http://www.elsevier.com/locate/eor

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Keywords: Relation algebra Rel View Simple game Winning coalition Dominant player Central player;

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References

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  1. Prasad, K & Kelly, J S, 1990. "NP-Completeness of Some Problems Concerning Voting Games," International Journal of Game Theory, Springer, vol. 19(1), pages 1-9.
  2. Rudolf Berghammer & Agnieszka Rusinowska & Harrie De Swart, 2009. "Applying Relation Algebra and RelView to Measures in aSocial Network," Post-Print halshs-00355699, HAL.
  3. repec:hal:cesptp:hal-00515878 is not listed on IDEAS
  4. Lorenzo-Freire, S. & Alonso-Meijide, J.M. & Casas-Mendez, B. & Fiestras-Janeiro, M.G., 2007. "Characterizations of the Deegan-Packel and Johnston power indices," European Journal of Operational Research, Elsevier, vol. 177(1), pages 431-444, February.
  5. Klinz, Bettina & Woeginger, Gerhard J., 2005. "Faster algorithms for computing power indices in weighted voting games," Mathematical Social Sciences, Elsevier, vol. 49(1), pages 111-116, January.
  6. Rudolf Berghammer & Agnieszka Rusinowska & Harrie De Swart, 2009. "An Interdisciplinary Approach to Coalition Formation," Post-Print halshs-00406460, HAL.
  7. R J Johnston, 1978. "On the measurement of power: some reactions to Laver," Environment and Planning A, Pion Ltd, London, vol. 10(8), pages 907-914, August.
  8. Berghammer, Rudolf & Rusinowska, Agnieszka & de Swart, Harrie, 2007. "Applying relational algebra and RelView to coalition formation," European Journal of Operational Research, Elsevier, vol. 178(2), pages 530-542, April.
  9. Lehrer, E, 1988. "An Axiomatization of the Banzhaf Value," International Journal of Game Theory, Springer, vol. 17(2), pages 89-99.
  10. Alonso-Meijide, J.M. & Casas-Mendez, B. & Holler, M.J. & Lorenzo-Freire, S., 2008. "Computing power indices: Multilinear extensions and new characterizations," European Journal of Operational Research, Elsevier, vol. 188(2), pages 540-554, July.
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Cited by:
  1. 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.
  2. repec:hal:cesptp:hal-00633857 is not listed on IDEAS
  3. repec:hal:cesptp:hal-00633859 is not listed on IDEAS
  4. Rudolf Berghammer & Agnieszka Rusinowska & Harrie de Swart, 2011. "Computations on Simple Games using REL VIEW," Documents de travail du Centre d'Economie de la Sorbonne 11014, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  5. 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.

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