Abstract
We demonstrate how relation algebra and a supporting tool can be combined to solve problems of voting systems. We model plurality voting within relation algebra and present relation-algebraic specifications for some computational tasks. They can be transformed immediately into the programming language of the BDD-based Computer Algebra system RelView, such that this tool can be used to solve the problems in question and to visualize the computed results. The approach is extremely formal, very flexible and especially appropriate for prototyping, experimentation, scientific research, and education.
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Bartholdi III, J.J., Tovey, C.A., Trick, M.A.: How hard is it to control an election? Mathematical and Computer Modeling 16, 27–40 (1992)
Berghammer, R., Neumann, F.: RelView – An OBDD-based Computer Algebra system for relations. In: Ganzha, V.G., Mayr, E.W., Vorozhtsov, E.V. (eds.) CASC 2005. LNCS, vol. 3718, pp. 40–51. Springer, Heidelberg (2005)
Berghammer, R., Winter, M.: Embedding mappings and splittings with applications. Acta Informatica 47, 77–110 (2010)
Berghammer, R., Danilenko, N., Schnoor, H.: Relation algebra and relView applied to approval voting. In: Höfner, P., Jipsen, P., Kahl, W., Müller, M.E. (eds.) RAMiCS 2014. LNCS, vol. 8428, pp. 309–326. Springer, Heidelberg (2014)
Berghammer, R., Höfner, P., Stucke, I.: Automated verification of relational while-programs. In: Höfner, P., Jipsen, P., Kahl, W., Müller, M.E. (eds.) RAMiCS 2014. LNCS, vol. 8428, pp. 173–190. Springer, Heidelberg (2014)
Berghammer, R., Schnoor, H.: Control of Condorcet voting: Complexity and a relation-algebraic approach (Extended abstract). In: Proc. AAMAS 2014 (to appear, 2014)
Brandt, F., Conitzer, V., Endriss, U.: Computational social choice. In: Weiss, G. (ed.) Multiagent Systems, 2nd edn., pp. 213–283. MIT Press (2013)
Faliszewski, P., Hemaspaandra, E., Hemaspaandra, L., Rothe, J.: Llull and Copeland voting computationally resist bribery and constructive control. Journal of Artificial Intelligence Research 35, 275–341 (2009)
Gansner, E.R., Koutsofios, E., North, S.C., Vo, K.P.: A technique for drawing directed graphs. IEEE Transactions on Software Engineering 19, 214–230 (1993)
Hemaspaandra, E., Hemaspaandra, L., Rothe, J.: Anyone but him: The complexity of precluding an alternative. Artificial Intelligence 171, 255–285 (2007)
Leoniuk, B.: ROBDD-based implementation of relational algebra with applications. Dissertation, Universität Kiel (2001) (in German)
Milanese, U.: On the implementation of a ROBDD-based tool for the manipulation and visualization of relations. Dissertation, Universität Kiel (2003) (in German)
Schmidt, G., Ströhlein, T.: Relations and graphs. Springer (1993)
Schmidt, G.: Relational mathematics. Cambridge University Press (2010)
RelView-homepage, http://www.informatik.uni-kiel.de/~progsys/relview/
Prover9-homepage, http://www.prover9.org
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Berghammer, R. (2014). Relation Algebra, RelView, and Plurality Voting. In: Gerdt, V.P., Koepf, W., Seiler, W.M., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2014. Lecture Notes in Computer Science, vol 8660. Springer, Cham. https://doi.org/10.1007/978-3-319-10515-4_2
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DOI: https://doi.org/10.1007/978-3-319-10515-4_2
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