An Interdisciplinary Approach to Coalition Formation Berghammer, Rudolf; Rusinowska, Agnieszka; De Swart, Harrie

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Berghammer, Rudolf ; Rusinowska, Agnieszka ; De Swart, Harrie
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European Journal of Operational Research
Computer Science; Algorithms; Algebra
Academic; Trade
To link to full-text access for this article, visit this link: Byline: Rudolf Berghammer (a), Agnieszka Rusinowska (b), Harrie de Swart (c) Keywords: Graph theory; RelView; Relational algebra; Dominance; Stable government Abstract: A stable government is by definition not dominated by any other government. However, it may happen that all governments are dominated. In graph-theoretic terms this means that the dominance graph does not possess a source. In this paper we are able to deal with this case by a clever combination of notions from different fields, such as relational algebra, graph theory and social choice theory, and by using the computer support system RelView for computing solutions and visualizing the results. Using relational algorithms, in such a case we break all cycles in each initial strongly connected component by removing the vertices in an appropriate minimum feedback vertex set. In this way we can choose a government that is as close as possible to being un-dominated. To achieve unique solutions, we additionally apply the majority ranking recently introduced by Balinski and Laraki. The main parts of our procedure can be executed using the RelView tool. Its sophisticated implementation of relations allows to deal with graph sizes that are sufficient for practical applications of coalition formation. Author Affiliation: (a) Institute of Computer Science, University of Kiel, Olshausenstra[sz]e 40, 24098 Kiel, Germany (b) GATE, CNRS, Universite Lumiere Lyon 2, 93 Chemin des Mouilles, B.P.167, 69131 Ecully Cedex, France (c) Department of Philosophy, Tilburg University, P.O. Box 90153, 5000 LE Tilburg, The Netherlands Article History: Received 4 December 2006; Accepted 12 February 2008 Article Note: (footnote) [star] Co-operation for this paper was supported by European COST Action 274 'Theory and Applications of Relational Structures as Knowledge Instruments' (TARSKI).
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