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Relation Algebra and RelView Applied to Approval Voting

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Relational and Algebraic Methods in Computer Science (RAMICS 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8428))

Abstract

In this paper we demonstrate how relation algebra and a BDD-based tool can be combined to solve computational problems of voting systems. We concentrate on approval voting and model this kind of voting within relation algebra. Based on this, we then formally develop relation-algebraic specifications of two important control problems from their logical specifications. They can be transformed immediately into the programming language of the BDD-based Computer Algebra system RelView. Therefore, this tool can be used to solve the problems and to visualize the computed results. The entire approach is extremely formal but also very flexible. In combination with RelView it is especially appropriate for prototyping and experimentation, and as such very instructive for educational purposes.

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References

  1. Bartholdi III, J.J., Tovey, C.A., Trick, M.A.: The computational difficulty of manipulating an election. Social Choice and Welfare 6, 227–241 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  2. 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)

    Article  MATH  MathSciNet  Google Scholar 

  3. 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)

    Chapter  Google Scholar 

  4. Brams, S.J., Fishburn, P.C.: Voting procedures. In: Arrow, K., Sen, A., Suzumara, K. (eds.) Handbook of Social Choice and Welfare, vol. 1, pp. 173–236. North-Holland (2002)

    Google Scholar 

  5. Brams, S.J., Fishburn, P.C.: Approval voting, 2nd edn. Springer (2007)

    Google Scholar 

  6. Brandt, F., Conitzer, V., Endriss, U.: Computational social choice. In: Weiss, G. (ed.) Multiagent Systems, 2nd edn., pp. 213–283. MIT Press (2013)

    Google Scholar 

  7. Chevaleyre, Y., Endriss, U., Lang, J., Maudet, N.: A short introduction to computational social choice. In: van Leeuwen, J., Italiano, G.F., van der Hoek, W., Meinel, C., Sack, H., Plášil, F. (eds.) SOFSEM 2007. LNCS, vol. 4362, pp. 51–69. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  8. Fischer S.: Tabulated binomial coefficients, http://www-ps.informatik.uni-kiel.de/~sebf/haskell/tabulated-binomial-coefficients.lhs.html

  9. Hemaspaandra, E., Hemaspaandra, L., Rothe, J.: Anyone but him: The complexity of precluding an alternative. Artificial Intelligence 171, 255–285 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  10. Laslier, J.-F.: And the loser is …plurality voting. In: Felsenthal, D.S., Machover, M. (eds.) Electoral Systems, Studies in Choice and Welfare, pp. 327–351. Springer (2012)

    Google Scholar 

  11. Leoniuk, B.: ROBDD-based implementation of relational algebra with applications. Dissertation, Universität Kiel (2001) (in German)

    Google Scholar 

  12. Milanese, U.: On the implementation of a ROBDD-based tool for the manipulation and visualization of relations. Dissertation, Universität Kiel (2003) (in German)

    Google Scholar 

  13. Nurmi, H.: On the difficulty of making social choices. Theory and Decision 38, 99–119 (1998)

    Article  Google Scholar 

  14. Schmidt, G., Ströhlein, T.: Relations and graphs, Discrete mathematics for computer scientists. EATCS Monographs on Theoretical Computer Science. Springer (1993)

    Google Scholar 

  15. Schmidt, G.: Relational mathematics. Encyclopedia of Mathematics and its Applications, vol. 132. Cambridge University Press (2010)

    Google Scholar 

  16. Walsh, T.: Is computational complexity a barrier to manipulation? Annals of Mathematics and Artificial Intelligence 62, 7–26 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  17. http://www.informatik.uni-kiel.de/~progsys/relview

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Berghammer, R., Danilenko, N., Schnoor, H. (2014). Relation Algebra and RelView Applied to Approval Voting. In: Höfner, P., Jipsen, P., Kahl, W., Müller, M.E. (eds) Relational and Algebraic Methods in Computer Science. RAMICS 2014. Lecture Notes in Computer Science, vol 8428. Springer, Cham. https://doi.org/10.1007/978-3-319-06251-8_19

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  • DOI: https://doi.org/10.1007/978-3-319-06251-8_19

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-06250-1

  • Online ISBN: 978-3-319-06251-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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