On Coalitions and Stable Winners in Plurality

  • Dvir Falik
  • Reshef Meir
  • Moshe Tennenholtz
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7695)

Abstract

We consider elections under the Plurality rule, where all voters are assumed to act strategically. As there are typically many Nash equilibria for every preference profile, and strong equilibria do not always exist, we analyze the most stable outcomes according to their stability scores (the number of coalitions with an interest to deviate). We show a tight connection between the Maximin score of a candidate and the highest stability score of the outcomes where this candidate wins, and show that under mild conditions the Maximin winner will also be the winner in the most stable outcome under Plurality.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bartholdi, J.J., Tovey, C.A., Trick, M.A.: The computational difficulty of manipulating an election. Social Choice and Welfare 6(3), 227–241 (1989)MathSciNetMATHCrossRefGoogle Scholar
  2. 2.
    Desmedt, Y., Elkind, E.: Equilibria of plurality voting with abstentions. In: EC 2010, pp. 347–356. ACM, New York (2010)Google Scholar
  3. 3.
    Feldman, M., Meir, R., Tennenholtz, M.: Stability scores: Measuring coalitional stability. In: AAMAS 2012, pp. 771–778 (2012)Google Scholar
  4. 4.
    Gibbard, A.: Manipulation of voting schemes. Econometrica 41, 587–602 (1973)MathSciNetMATHCrossRefGoogle Scholar
  5. 5.
    Kalai, G.: A fourier-theoretic perspective for the condorcet paradox and arrow’s theorem. Advances in Applied Mathematics 29(3), 412–426 (2001)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Kukushkin, N.: Acyclicity of improvements in finite game forms. International Journal of Game Theory 40, 147–177 (2011)MathSciNetMATHCrossRefGoogle Scholar
  7. 7.
    Meir, R., Polukarov, M., Rosenschein, J.S., Jennings, N.: Convergence to equilibria of plurality voting. In: AAAI 2010, Atlanta, Georgia, pp. 823–828 (July 2010)Google Scholar
  8. 8.
    Messner, M., Polborn, M.K.: Robust political equilibria under plurality and runoff rule. Bocconi University, Mimeo (2002)Google Scholar
  9. 9.
    Mossel, E., Racz, M.Z.: A quantitative gibbard-satterthwaite theorem without neutrality. In: STOC 2012, pp. 1041–1060 (2012)Google Scholar
  10. 10.
    Myerson, R.B., Weber, R.J.: A theory of voting equilibria. The American Political Science Review 87(1), 102–114 (1993)CrossRefGoogle Scholar
  11. 11.
    Peleg, B.: Game-theoretic analysis of voting in committees. In: Sen, A.K., Arrow, K.J., Suzumura, K. (eds.) Handbook of Social Choice and Welfare, ch. 8, vol. 1, Elsevier Science B (2002)Google Scholar
  12. 12.
    Procaccia, A.D., Rosenschein, J.S.: Average-case tractability of manipulation in voting via the fraction of manipulators. In: AAMAS 2007 (2007)Google Scholar
  13. 13.
    Satterthwaite, M.: Strategy-proofness and Arrow’s conditions: Existence and correspondence theorems for voting procedures and social welfare functions. Journal of Economic Theory 10, 187–217 (1975)MathSciNetMATHCrossRefGoogle Scholar
  14. 14.
    Sertel, M.R., Remzi Sanver, M.: Strong equilibrium outcomes of voting games are the generalized condorcet winners. Social Choice and Welfare 22, 331–347 (2004)MathSciNetMATHCrossRefGoogle Scholar
  15. 15.
    De Sinopoli, F.: Sophisticated voting and equlibrium refinements under plurality rule. Social Choice and Welfare 17, 655–672 (2000)MathSciNetMATHCrossRefGoogle Scholar
  16. 16.
    De Sinopoli, F.: On the generic finiteness of equilibrium outcomes in plurality games. Games and Economic Behavior 34, 270–286 (2001)MathSciNetMATHCrossRefGoogle Scholar
  17. 17.
    Thompson, D.R.M., Lev, O., Leyton-Brown, K., Rosenschein, J.S.: Empirical aspects of plurality election equilibria. In: COMSOC 2012 (2012)Google Scholar
  18. 18.
    Xia, L.: Computing the margin of victory for various voting rules. In: EC 2012, pp. 982–999 (2012)Google Scholar
  19. 19.
    Xia, L., Conitzer, V.: Generalized scoring rules and the frequency of coalitional manipulability. In: EC 2008, pp. 109–118 (2008)Google Scholar
  20. 20.
    Xia, L., Conitzer, V.: Stackelberg voting games: Computational aspects and paradoxes. In: AAAI 2010, Atlanta, Georgia, pp. 921–926 (July 2010)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Dvir Falik
    • 1
  • Reshef Meir
    • 2
    • 3
  • Moshe Tennenholtz
    • 2
    • 4
  1. 1.Tel-Aviv UniversityTel-AvivIsrael
  2. 2.Microsoft ResearchHerzliaIsrael
  3. 3.Hebrew UniversityJerusalemIsrael
  4. 4.Technion-Israel Institute of TechnologyIsrael

Personalised recommendations