Correlated Voting

We study the social choice problem where a group of n voters report their preferences over alternatives and a voting rule is used to select an alternative. We show that when the preferences of voters are positively correlated according to the Kendall-Tau distance, the probability that any scoring rule is not ex post incentive compatible (EPIC) goes to zero exponentially fast with the number of voters, improving over the previously known rate of 1/√n for independent preferences. Motivated by rank-order models from machine learning, we introduce two examples of positively-correlated models, namely Conditional Mallows and Conditional Plackett-Luce. Conditional Mallows satisfies Kendall-Tau correlation and fits our positive result. We also prove that Conditional Plackett-Luce becomes EPIC exponentially quickly.

[1]  Z. Neeman,et al.  The asymptotic strategyproofness of scoring and Condorcet consistent rules , 2002 .

[2]  K. Arrow,et al.  Handbook of Social Choice and Welfare , 2011 .

[3]  Lirong Xia,et al.  Sequential composition of voting rules in multi-issue domains , 2009, Math. Soc. Sci..

[4]  Arunava Sen,et al.  Ordinally Bayesian incentive compatible voting rules , 2004 .

[5]  D. A. Bell,et al.  Applied Statistics , 1953, Nature.

[6]  W. Hoeffding.  Probability Inequalities for sums of Bounded Random Variables , 1963 .

[7]  M. Satterthwaite.  Strategy-proofness and Arrow's conditions: Existence and correspondence theorems for voting procedures and social welfare functions , 1975 .

[8]  Eric Horvitz,et al.  Social Choice Theory and Recommender Systems: Analysis of the Axiomatic Foundations of Collaborative Filtering , 2000, AAAI/IAAI.

[9]  Moshe Tennenholtz,et al.  An axiomatic approach to personalized ranking systems , 2007, JACM.

[10]  Peter C. Fishburn,et al.  Theory and decision , 2003 .

[11]  R. Luce,et al.  Individual Choice Behavior: A Theoretical Analysis. , 1960 .

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

[13]  R. Durrett.  Probability: Theory and Examples , 1993 .

[14]  R. Fildes.  Journal of the American Statistical Association : William S. Cleveland, Marylyn E. McGill and Robert McGill, The shape parameter for a two variable graph 83 (1988) 289-300 , 1989 .

[15]  R. Plackett.  The Analysis of Permutations , 1975 .

[16]  Ariel D. Procaccia,et al.  Beyond Dominant Resource Fairness , 2015, ACM Trans. Economics and Comput..

[17]  Piotr Faliszewski,et al.  AI's War on Manipulation: Are We Winning? , 2010, AI Mag..

[18]  Lawrence G. Sager.  Handbook of Computational Social Choice , 2015 .

[19]  S. Barberà.  Chapter Twenty-Five - Strategyproof Social Choice , 2011 .

[20]  D. Hunter.  MM algorithms for generalized Bradley-Terry models , 2003 .

[21]  R. Duncan Luce,et al.  Individual Choice Behavior: A Theoretical Analysis , 1979 .

[22]  K. Pearson,et al.  Biometrika , 1902, The American Naturalist.

[23]  Arkadii Slinko,et al.  On Asymptotic Strategy-Proofness of Classical Social Choice Rules , 2002 .

[24]  Arunava Sen,et al.  Incentive-compatible voting rules with positively correlated beliefs , 2015 .

[25]  Vincent Conitzer,et al.  Barriers to Manipulation in Voting , 2016, Handbook of Computational Social Choice.

[26]  S. Weintraub,et al.  Theoretical Economics , 1964 .

[27]  Ariel D. Procaccia,et al.  Better Human Computation Through Principled Voting , 2013, AAAI.

[28]  H. Young.  Social Choice Scoring Functions , 1975 .

[29]  A. Gibbard.  Manipulation of Voting Schemes: A General Result , 1973 .