A relation-algebraic approach to simple games |
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| Authors: | Rudolf Berghammer Stefan Bolus Agnieszka Rusinowska Harrie de Swart |
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| Institution: | 1. Institut für Informatik, Universität Kiel Olshausenstraße 40, 24098 Kiel, Germany;2. Centre d’Economie de la Sorbonne, CNRS - Université Paris I Panthéon-Sorbonne 106-112 Bd de l’Hôpital, 75647 Paris Cedex 13, France;3. Department of Philosophy, Tilburg University, P.O. Box 90153, 5000 LE Tilburg, The Netherlands |
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| 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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| Keywords: | Relation algebra Rel View Simple game Winning coalition Dominant player Central player |
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