Advertisement

A Ranking Procedure with the Shapley Value

  • Aleksei Kondratev
  • Vladimir Mazalov
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10192)

Abstract

This paper considers the problem of electing candidates for a certain position based on ballots filled by voters. We suggest a voting procedure using cooperative game theory methods. For this, it is necessary to construct a characteristic function via the preference profile of voters. The Shapley value serves as the ranking method. The winner is the candidate having the maximum Shapley value. And finally, we explore the properties of the designed procedures.

Keywords

Tournament matrix Shapley value Preference aggregation rule Voting procedure Condorcet criterion Characteristic function 

Notes

Acknowledgments

This work is supported by the Russian Humanitarian Science Foundation (grant 15-02-00352_a) and the Russian Fund for Basic Research (project 16-51-55006 China_a).

References

  1. 1.
    Arrow, K.J.: Social Choice and Individual Values, vol. 12. Yale University Press, New Haven (2012)zbMATHGoogle Scholar
  2. 2.
    Balinski, M., Laraki, R.: A theory of measuring, electing, and ranking. Proc. Natl. Acad. Sci. 104(21), 8720–8725 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Brams, S.J.: Mathematics and Democracy: Designing Better Voting and Fair-Division Procedures. Prinston University Press, Princeton (2007)zbMATHGoogle Scholar
  4. 4.
    Brams, S.J., Fishburn, P.C.: Going from theory to practice: the mixed success of approval voting. Soc. Choice Welf. 25(2–3), 457–474 (2005)CrossRefzbMATHGoogle Scholar
  5. 5.
    Brandt, F., Brill, M., Harrenstein, P.: Tournament solutions. Handbook of Computational Social Choice (2009)Google Scholar
  6. 6.
    Copeland, A.H.: A reasonable social welfare function (mimeo). University of Michigan, Ann Arbor (Seminar on Application of Mathematics to the Social Sciences) (1951)Google Scholar
  7. 7.
    Gaertner, W., Xu, Y.: A general scoring rule. Math. Soc. Sci. 63(3), 193–196 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Hillinger, C.: The case for utilitarian voting. Homo Oeconomicus 22(3), 295–321 (2005)Google Scholar
  9. 9.
    Schulze, M.A.: New monotonic, clone-independent, reversal symmetric, and condorcet-consistent single-winner election method. Soc. Choice Welf. 36(2), 267–303 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Tideman, T.N.: Independence of clones as a criterion for voting rules. Soc. Choice Welf. 4(3), 185–206 (1987)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Young, H.P.: Group choice and individual judgements. In: Mueller, D. (ed.) Perspectives on Public Choice: A Handbook, pp. 181–200. Cambridge University Press, Cambridge (1997)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Russian Academy of Sciences, Karelian Research Center, Institute of Applied Mathematical ResearchPetrozavodskRussia

Personalised recommendations