On the Discriminative Power of Tournament Solutions

  • Felix Brandt
  • Hans Georg Seedig
Conference paper
Part of the Operations Research Proceedings book series (ORP)


Tournament solutions constitute an important class of social choice functions that only depend on the pairwise majority comparisons between alternatives. Recent analytical results have shown that several concepts with appealing axiomatic properties tend to not discriminate at all when the tournaments are chosen from the uniform distribution. This is in sharp contrast to empirical studies which have found that real-world preference profiles often exhibit Condorcet winners, i.e., alternatives that all tournament solutions select as the unique winner. In this work, we aim to fill the gap between these extremes by examining the distribution of the number of alternatives returned by common tournament solutions for empirical data as well as data generated according to stochastic preference models.


  1. 1.
    Berg, S.: Paradox of voting under an urn model: the effect of homogeneity. Public Choice 47, 377–387 (1985)CrossRefGoogle Scholar
  2. 2.
    Brandt, F., Conitzer, V., Endriss, U.: Computational social choice. In: Weiß, G. (ed.) Multiagent Systems, chapter 6, 2nd edn., pp. 213–283. MIT Press (2013)Google Scholar
  3. 3.
    Brandt, F., Dau, A., Seedig, H.G.: Bounds on the disparity and separation of tournament solutions. Discrete Appl. Math. 187, 41–49 (2015)Google Scholar
  4. 4.
    Critchlow, D.E., Fligner, M.A., Verducci, J.S.: Probability models on rankings. J. Math. Psychol. 35, 294–318 (1991)CrossRefGoogle Scholar
  5. 5.
    Fey, M.: Choosing from a large tournament. Soc. Choice Welfare 31(2), 301–309 (2008)CrossRefGoogle Scholar
  6. 6.
    Fisher, D.C., Reeves, R.B.: Optimal strategies for random tournament games. Linear Algebra Appl. 217, 83–85 (1995)CrossRefGoogle Scholar
  7. 7.
    Laslier, J.-F.: Tournament Solutions and Majority Voting. Springer (1997)Google Scholar
  8. 8.
    Laslier, J.-F.: In silico voting experiments. In: Laslier, J.-F., Sanver, M.R. (eds.) Handbook on Approval Voting, chapter 13, pp. 311–335. Springer-Verlag (2010)Google Scholar
  9. 9.
    Mallows, C.L.: Non-null ranking models. Biometrika 44(1/2), 114–130 (1957)CrossRefGoogle Scholar
  10. 10.
    Mattei, N., Walsh, T.: PrefLib: A library for preference data. In: Proceedings of 3rd ADT, vol. 8176 of Lecture Notes in Computer Science (LNCS), pp. 259–270. Springer (2013).
  11. 11.
    McCabe-Dansted, J.C., Slinko, A.: Exploratory analysis of similarities between social choice rules. Group Decis. Negot. 15(1), 77–107 (2006)CrossRefGoogle Scholar
  12. 12.
    Ordeshook, P. C.: The spatial analysis of elections and committees: four decades of research. Technical report, California Institute of Technology. Mimeo (1993)Google Scholar
  13. 13.
    Regenwetter, M., Grofman, B., Marley, A.A.J., Tsetlin, I.M.: Behavioral Social Choice: Probabilistic Models, Statistical Inference, and Applications. Cambridge University Press (2006)Google Scholar
  14. 14.
    Scott, A., Fey, M.: The minimal covering set in large tournaments. Soc. Choice Welfare 38(1), 1–9 (2012)CrossRefGoogle Scholar
  15. 15.
    Seedig, H.G.: Majority Relations and Tournament Solutions: A Computational Study. Ph.D. thesis, Technische Universität München (2015)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Institut für InformatikTechnische Universität MünchenMünchenGermany

Personalised recommendations