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A Relation-algebraic Approach to Simple Games

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Author Info

  • Rudolf Berghammer

    (Computer-Aided Program Development - Institute of Computer Science - Christian-Albrechts-Universität zu Kiel)

  • Harrie De Swart

    (Faculteit Wijsbegeerte-Logica en taalanalyse - Universiteit van Tilburg)

  • Agnieszka Rusinowska

    ()
    (GATE - Groupe d'analyse et de théorie économique - CNRS : UMR5824 - Université Lumière - Lyon II - Ecole Normale Supérieure Lettres et Sciences Humaines)

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 algorithms for solving some basic problems of them. In particular, we test certain fundamental properties of simple games (being monotone, proper, respectively strong) and compute specific players (dummies, dictators, vetoers, null players) and coalitions (minimal winning coalitions and vulnerable winning coalitions). We also apply relation-algebra to determine central and dominant players, swingers and power indices (the Banzhaf, Holler-Packel and Deegan-Packel indices). This leads to relation-algebraic specifications, which can be executed with the help of the BDD-based tool RelView after a simple translation into the tool's programming language. In order to demonstrate the visualization facilities of RelView we consider an example of the Catalonian Parliament after the 2003 election.

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Bibliographic Info

Paper provided by HAL in its series Post-Print with number halshs-00404398.

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Date of creation: 2011
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Publication status: Published, European Journal of Operational Research, 2011, 210, 1, pp. 68-80
Handle: RePEc:hal:journl:halshs-00404398

Note: View the original document on HAL open archive server: http://halshs.archives-ouvertes.fr/halshs-00404398/en/
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Related research

Keywords: relation algebra; RelView; simple game; winning coalition; swinger; dominant player; central player; power index;

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References

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  1. 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.
  2. Rudolf Berghammer & Agnieszka Rusinowska & Harrie De Swart, 2009. "An Interdisciplinary Approach to Coalition Formation," Post-Print halshs-00406460, HAL.
  3. 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.
  4. 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.
  5. 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.
  6. repec:hal:cesptp:hal-00515878 is not listed on IDEAS
  7. Rudolf Berghammer & Agnieszka Rusinowska & Harrie De Swart, 2009. "Applying Relation Algebra and RelView to Measures in aSocial Network," Post-Print halshs-00355699, HAL.
  8. Rudolf Berghammer & Harrie De Swart & Agnieszka Rusinowska, 2007. "Applying relational algebra and RelView to coalition formation," Post-Print halshs-00159845, HAL.
  9. 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.
  10. Lehrer, E, 1988. "An Axiomatization of the Banzhaf Value," International Journal of Game Theory, Springer, vol. 17(2), pages 89-99.
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Cited by:
  1. repec:hal:cesptp:hal-00633859 is not listed on IDEAS
  2. repec:hal:cesptp:halshs-00587690 is not listed on IDEAS
  3. repec:hal:cesptp:hal-00633857 is not listed on IDEAS
  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. 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.
  6. 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.

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