Ranked Voting on Social Networks

Classic social choice theory assumes that votes are independent (but possibly conditioned on an underlying objective ground truth). This assumption is unrealistic in settings where the voters are connected via an underlying social network structure, as social interactions lead to correlated votes. We establish a general framework -- based on random utility theory -- for ranked voting on a social network with arbitrarily many alternatives (in contrast to previous work, which is restricted to two alternatives). We identify a family of voting rules which, without knowledge of the social network structure, are guaranteed to recover the ground truth with high probability in large networks, with respect to a wide range of models of correlation among input votes.

[1]  F. Mosteller.  Remarks on the method of paired comparisons: I. The least squares solution assuming equal standard deviations and equal correlations , 1951 .

[2]  David C. Parkes,et al.  Computing Parametric Ranking Models via Rank-Breaking , 2014, ICML.

[3]  Elchanan Mossel,et al.  Majority dynamics and aggregation of information in social networks , 2012, Autonomous Agents and Multi-Agent Systems.

[4]  Ariel D. Procaccia,et al.  A Maximum Likelihood Approach For Selecting Sets of Alternatives , 2012, UAI.

[5]  Ariel D. Procaccia,et al.  When do noisy votes reveal the truth? , 2013, EC '13.

[6]  Vincent Conitzer,et al.  Communication complexity of common voting rules , 2005, EC '05.

[7]  L. Thurstone,et al.  A low of comparative judgement , 1927 .

[8]  Leandro Soriano Marcolino,et al.  Diverse Randomized Agents Vote to Win , 2014, NIPS.

[9]  Vincent Conitzer,et al.  Aggregating preferences in multi-issue domains by using maximum likelihood estimators , 2010, AAMAS.

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

[11]  F. Mosteller.  Remarks on the method of paired comparisons: I. The least squares solution assuming equal standard deviations and equal correlations , 1951 .

[12]  David C. Parkes,et al.  Preference Elicitation For General Random Utility Models , 2013, UAI.

[13]  Vincent Conitzer.  Should social network structure be taken into account in elections? , 2012, Math. Soc. Sci..

[14]  H. Young.  Condorcet's Theory of Voting , 1988, American Political Science Review.

[15]  Vincent Conitzer,et al.  A Maximum Likelihood Approach towards Aggregating Partial Orders , 2011, IJCAI.

[16]  Elchanan Mossel.  Gaussian Bounds for Noise Correlation of Functions , 2007, FOCS 2007.

[17]  Craig Boutilier,et al.  Robust Approximation and Incremental Elicitation in Voting Protocols , 2011, IJCAI.

[18]  M. Degroot.  Reaching a Consensus , 1974 .

[19]  David C. Parkes,et al.  Random Utility Theory for Social Choice , 2012, NIPS.

[20]  Ariel D. Procaccia,et al.  Modal Ranking: A Uniquely Robust Voting Rule , 2014, AAAI.

[21]  Aryeh Kontorovich,et al.  Concentration in unbounded metric spaces and algorithmic stability , 2013, ICML.

[22]  Vincent Conitzer.  The maximum likelihood approach to voting on social networks , 2013, 2013 51st Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[23]  L. Thurstone.  A law of comparative judgment. , 1994 .

[24]  J. Kleinberg.  Algorithmic Game Theory: Cascading Behavior in Networks: Algorithmic and Economic Issues , 2007 .

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

[26]  Piotr Faliszewski,et al.  Good Rationalizations of Voting Rules , 2010, AAAI.