On the Discriminative Power of Tournament Solutions

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]  Mark Fey,et al.  Choosing from a large tournament , 2008, Soc. Choice Welf..

[2]  Alex D. Scott,et al.  The minimal covering set in large tournaments , 2012, Soc. Choice Welf..

[3]  Craig Boutilier,et al.  Learning Mallows Models with Pairwise Preferences , 2011, ICML.

[4]  C. Plott,et al.  The Probability of a Cyclical Majority , 1970 .

[5]  Felix Brandt,et al.  Minimal stable sets in tournaments , 2008, J. Econ. Theory.

[6]  Felix Brandt,et al.  Necessary and sufficient conditions for the strategyproofness of irresolute social choice functions , 2011, TARK XIII.

[7]  Scott L. Feld,et al.  Who's Afraid of the Big Bad Cycle? Evidence from 36 Elections , 1992 .

[8]  C. L. Mallows NON-NULL RANKING MODELS. I , 1957 .

[9]  P. Ordeshook The Spatial Analysis of Elections and Committees: Four Decades of Research , 1993 .

[10]  A. A. J. Marley,et al.  Behavioral Social Choice - Probabilistic Models, Statistical Inference, and Applications , 2006 .

[11]  J. Banks,et al.  Positive Political Theory I: Collective Preference , 1998 .

[12]  David C. Fisher,et al.  Optimal strategies for random tournament games , 1995 .

[13]  J. Marden Analyzing and Modeling Rank Data , 1996 .

[14]  Jean-François Laslier,et al.  Tournament Solutions And Majority Voting , 1997 .

[15]  Felix Brandt,et al.  Minimal retentive sets in tournaments , 2014, Soc. Choice Welf..

[16]  Toby Walsh,et al.  PrefLib: A Library for Preferences http://www.preflib.org , 2013, ADT.

[17]  Olivier Hudry,et al.  A survey on the complexity of tournament solutions , 2009, Math. Soc. Sci..

[18]  Michel Truchon,et al.  Maximum likelihood approach to vote aggregation with variable probabilities , 2004, Soc. Choice Welf..

[19]  F. Brandt,et al.  Computational Social Choice: Prospects and Challenges , 2011, FET.

[20]  A. Pekec,et al.  The repeated insertion model for rankings: Missing link between two subset choice models , 2004 .

[21]  A. Slinko,et al.  Exploratory Analysis of Similarities Between Social Choice Rules , 2006 .

[22]  Jean-François Laslier,et al.  In Silico Voting Experiments , 2010 .

[23]  Joseph S. Verducci,et al.  Probability models on rankings. , 1991 .

[24]  Felix Brandt,et al.  Bounds on the disparity and separation of tournament solutions , 2015, Discret. Appl. Math..

[25]  Susan A. Murphy,et al.  Monographs on statistics and applied probability , 1990 .

[26]  H. Moulin Choosing from a tournament , 1986 .

[27]  Felix Brandt,et al.  Tournament Solutions Extensions of Maximality and their Applications to Decision-Making , 2009 .

[28]  Felix Brandt,et al.  Group-Strategyproof Irresolute Social Choice Functions , 2010, IJCAI.

[29]  P. Gärdenfors Manipulation of social choice functions , 1976 .

[30]  S. Berg Paradox of voting under an urn model: The effect of homogeneity , 1985 .