Abstract
We present an overview of the potential of relation algebra and the software tool RelView, based on it, to compute solutions for problems from social choice. Using one leading example throughout the text, we subsequently show how the RelView tool may be used to compute and visualize minimal winning coalitions, swingers of a given coalition, vulnerable winning coalitions, central players, dominant players, Banzhaf power indices of the different players, Hoede Bakker indices of the different players in a network, and finally stable coalitions/governments. Although problems from social choice and games are mostly exponential, due to the BDD implementation of RelView, computations are feasible for the examples which appear in practice.
Co-operation for this paper is supported by European Science Foundation EUROCORES Programme - LogICCC.
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References
Banzhaf, J.F.: Weighted Voting Doesn’t Work: A Mathematical Analysis. Rutgers Law Review 19, 317–343 (1965)
Berghammer, R., Rusinowska, A., de Swart, H.: Applying Relational Algebra and RelView to Coalition Formation. European Journal of Operational Research 178, 530–542 (2007)
Berghammer, R., Rusinowska, A., de Swart, H.: An Interdisciplinary Approach to Coalition Formation. European Journal of Operational Research 195, 487–496 (2009)
Berghammer, R., Rusinowska, A., de Swart, H.: Applying Relation Algebra and RelView to Measures in a Social Network. European Journal of Operational Research (to appear)
Berghammer, R., Rusinowska, A., de Swart, H.: A Relation-algebraic Approach to Simple Games (submitted for publication)
Coleman, J.S.: Control of Collectivities and the Power of a Collectivity to Act. In: Lieberman, Gordon, Breach, Social Choice, London (1971)
Coleman, J.S.: Individual Interests and Collective Action: Selected Essays. Cambridge University Press, Cambridge (1986)
Grabisch, M., Rusinowska, A.: A Model of Influence in a Social Network. Theory and Decision (to appear)
Hoede, C., Bakker, R.: A Theory of Decisional Power. Journal of Mathematical Sociology 8, 309–322 (1982)
Peleg, B.: Coalition Formation in Simple Games with Dominant Players. International Journal of Game Theory 10, 11–33 (1981)
Peleg, B., Sudhölter, P.: Introduction to the Theory of Cooperative Games. Springer, New York (2003)
Peters, H.: Game Theory: A Multi-leveled Approach. Springer, Berlin (2008)
Rae, D.: Decision Rules and Individual Values in Constitutional Choice. American Political Science Review 63, 40–56 (1969)
Roubens, M., Rusinowska, A., Swart, H.: Using MACBETH to Determine Utilities of Governments to Parties in Coalition Formation. European Journal of Operational Research 172, 588–603 (2006)
Rusinowska, A., de Swart, H.: Generalizing and Modifying the Hoede-Bakker Index. In: de Swart, H., Orłowska, E., Schmidt, G., Roubens, M. (eds.) TARSKI 2006. LNCS (LNAI), vol. 4342, pp. 60–88. Springer, Heidelberg (2006)
Rusinowska, A., de Swart, H., van der Rijt, J.W.: A New Model of Coalition Formation. Social Choice and Welfare 24, 129–154 (2005)
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de Swart, H., Berghammer, R., Rusinowska, A. (2009). Computational Social Choice Using Relation Algebra and RelView . In: Berghammer, R., Jaoua, A.M., Möller, B. (eds) Relations and Kleene Algebra in Computer Science. RelMiCS 2009. Lecture Notes in Computer Science, vol 5827. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04639-1_2
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DOI: https://doi.org/10.1007/978-3-642-04639-1_2
Publisher Name: Springer, Berlin, Heidelberg
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