Margin of Victory in Tournaments: Structural and Experimental Results

Tournament solutions are standard tools for identifying winners based on pairwise comparisons between competing alternatives. The recently studied notion of margin of victory (MoV) offers a general method for refining the winner set of any given tournament solution, thereby increasing the discriminative power of the solution. In this paper, we reveal a number of structural insights on the MoV by investigating fundamental properties such as monotonicity and consistency with respect to the covering relation. Furthermore, we provide experimental evidence on the extent to which the MoV notion refines winner sets in tournaments generated according to various stochastic models.

[1]  Stephanie Kovalchik,et al.  Extension of the Elo rating system to margin of victory , 2020 .

[2]  Felix Brandt,et al.  Tournament Solutions , 2016, Handbook of Computational Social Choice.

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

[4]  Arun Rajkumar,et al.  Dueling Bandits: Beyond Condorcet Winners to General Tournament Solutions , 2016, NIPS.

[5]  Gerhard J. Woeginger,et al.  Banks winners in tournaments are difficult to recognize , 2003, Soc. Choice Welf..

[6]  Weibin Han,et al.  A refinement of the uncovered set in tournaments , 2018, Theory and Decision.

[7]  Felix Brandt,et al.  Extending tournament solutions , 2014, Social Choice and Welfare.

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

[9]  Palash Dey.  Query Complexity of Tournament Solutions , 2017, AAAI.

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

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

[12]  Ulrike Schmidt-Kraepelin,et al.  Refining Tournament Solutions via Margin of Victory , 2019, AAAI.

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

[14]  Krishna P. Gummadi,et al.  Minimizing Margin of Victory for Fair Political and Educational Districting , 2019, AAMAS.

[15]  Warut Suksompong,et al.  Robust bounds on choosing from large tournaments , 2018, Social Choice and Welfare.

[16]  Felix A. Fischer,et al.  Possible and necessary winners of partial tournaments , 2012, AAMAS.

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

[18]  D. R. Fulkerson,et al.  Maximal Flow Through a Network , 1956 .

[19]  Felix Brandt,et al.  On the Discriminative Power of Tournament Solutions , 2014, OR.

[20]  Abelard Podgorski.  Tournament Decision Theory , 2020 .

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

[22]  Yongjie Yang,et al.  Possible Winner Problems on Partial Tournaments: A Parameterized Study , 2013, ADT.

[23]  Felix A. Fischer,et al.  PageRank as a Weak Tournament Solution , 2007, WINE.

[24]  Felix Brandt,et al.  A note on the McKelvey uncovered set and Pareto optimality , 2016, Soc. Choice Welf..

[25]  Jennifer Ryan,et al.  Tournament games and positive tournaments , 1995, J. Graph Theory.

[26]  Felix Brandt,et al.  On the structure of stable tournament solutions , 2016, Economic Theory.