Scalable Preference Aggregation in Social Networks IFCAM Workshop - PowerPoint PPT Presentation

Scalable Preference Aggregation in Social Networks IFCAM Workshop on Social Networks Indian Institute of Science, Bangalore Y. Narahari Joint work with Swapnil Dhamal Game Theory Lab Department of Computer Science and Automation Indian Institute of Science, Bangalore January 16, 2014 Y. Narahari (IISc) Scalable Preference Aggregation in Social Networks January 16, 2014 0 / 24

Overview Introduction and Motivation 1 A Sample Survey 2 Problem Formulation 3 Experimental Results 4 Conclusions 5 Y. Narahari (IISc) Scalable Preference Aggregation in Social Networks January 16, 2014 0 / 24

Overview Introduction and Motivation 1 A Sample Survey 2 Problem Formulation 3 Experimental Results 4 Conclusions 5 Y. Narahari (IISc) Scalable Preference Aggregation in Social Networks January 16, 2014 0 / 24

Homophily in Social Networks What constitutes a social network? Individuals and friendships Y. Narahari (IISc) Scalable Preference Aggregation in Social Networks January 16, 2014 1 / 24

Homophily in Social Networks What constitutes a social network? Individuals and friendships What causes friendships? Similarity of individuals Y. Narahari (IISc) Scalable Preference Aggregation in Social Networks January 16, 2014 1 / 24

Homophily in Social Networks What constitutes a social network? Individuals and friendships What causes friendships? Similarity of individuals What do friendships cause? Individuals become more similar Y. Narahari (IISc) Scalable Preference Aggregation in Social Networks January 16, 2014 1 / 24

Homophily in Social Networks What constitutes a social network? Individuals and friendships What causes friendships? Similarity of individuals What do friendships cause? Individuals become more similar What is homophily? A bias in friendships towards similar individuals Y. Narahari (IISc) Scalable Preference Aggregation in Social Networks January 16, 2014 1 / 24

Homophily in Social Networks What constitutes a social network? Individuals and friendships What causes friendships? Similarity of individuals What do friendships cause? Individuals become more similar What is homophily? A bias in friendships towards similar individuals Homophily plays a key role in social networks. Y. Narahari (IISc) Scalable Preference Aggregation in Social Networks January 16, 2014 1 / 24

Preference Aggregation Agents or Voters have certain preferences over a set of Alternatives Y Z X i X Y Z j Y X Z p Y. Narahari (IISc) Scalable Preference Aggregation in Social Networks January 16, 2014 2 / 24

Preference Aggregation Preference of a voter is a complete ranked list of alternatives Preference of voter i Y Z X i X Y Z j Y X Z p Y. Narahari (IISc) Scalable Preference Aggregation in Social Networks January 16, 2014 2 / 24

Preference Aggregation Preference Profile P is a vector of preferences of voters Preference of voter i Y Z X i X Y Z j Y X Z p Preference Profile Y. Narahari (IISc) Scalable Preference Aggregation in Social Networks January 16, 2014 2 / 24

Preference Aggregation Aggregation Rule f outputs an aggregate preference for each preference profile Preference of voter i Y Z X Aggregation Rule i Plurality X Y Z Y X Z j Y X Z p Preference Profile Y. Narahari (IISc) Scalable Preference Aggregation in Social Networks January 16, 2014 2 / 24

Preference Aggregation Aggregate Preference f ( P ) summarizes the preferences of the voters Preference of voter i Y Z X Aggregation Rule i Plurality X Y Z Y X Z j Y X Z p Aggregate Preference Preference Profile Y. Narahari (IISc) Scalable Preference Aggregation in Social Networks January 16, 2014 2 / 24

Normalized Kendall-Tau Distance r = number of alternatives Normalized Kendall-Tau Distance = Number of pair inversions � r � 2 Distance between ( X , Y , Z ) and ( X , Z , Y ) is 1 3 Distance between ( X , Y , Z ) and ( Y , Z , X ) is 2 3 Distance between ( X , Y , Z ) and ( Z , Y , X ) is 1 Y. Narahari (IISc) Scalable Preference Aggregation in Social Networks January 16, 2014 3 / 24

Motivation for the Work Many situations where we need to obtain a satisfactory aggregate preference given the individual preferences: meetings, committees, voting, poll surveys, product ranking, search engine aggregation, collaborative filtering, etc. Y. Narahari (IISc) Scalable Preference Aggregation in Social Networks January 16, 2014 4 / 24

Motivation for the Work Many situations where we need to obtain a satisfactory aggregate preference given the individual preferences: meetings, committees, voting, poll surveys, product ranking, search engine aggregation, collaborative filtering, etc. For large networks, it is infeasible to gather the preferences from all the voters due to a variety of factors: time, lack of interest of the voters, etc. Y. Narahari (IISc) Scalable Preference Aggregation in Social Networks January 16, 2014 4 / 24

Motivation for the Work Many situations where we need to obtain a satisfactory aggregate preference given the individual preferences: meetings, committees, voting, poll surveys, product ranking, search engine aggregation, collaborative filtering, etc. For large networks, it is infeasible to gather the preferences from all the voters due to a variety of factors: time, lack of interest of the voters, etc. Most interesting aggregation rules are computationally intensive Estimate the aggregate preference of the population by selecting a subset of voters, taking into account the social network Y. Narahari (IISc) Scalable Preference Aggregation in Social Networks January 16, 2014 4 / 24

Current Art and Research Gaps (1) Social networks do influence voting in elections 1 2 1 Sheingold, C. A. 1973. Social networks and voting: the resurrection of a research agenda. American Sociological Review 712-720. 2 Burstein, P. 1976. Social networks and voting: Some Israeli data. Social Forces 54(4):833–847. 3 Conitzer, V. 2012. Should social network structure be taken into account in elections? Mathematical Social Sciences 64(1):100-102. Y. Narahari (IISc) Scalable Preference Aggregation in Social Networks January 16, 2014 5 / 24

Current Art and Research Gaps (1) Social networks do influence voting in elections 1 2 Network structure can be ignored in many contexts 3 1 Sheingold, C. A. 1973. Social networks and voting: the resurrection of a research agenda. American Sociological Review 712-720. 2 Burstein, P. 1976. Social networks and voting: Some Israeli data. Social Forces 54(4):833–847. 3 Conitzer, V. 2012. Should social network structure be taken into account in elections? Mathematical Social Sciences 64(1):100-102. Y. Narahari (IISc) Scalable Preference Aggregation in Social Networks January 16, 2014 5 / 24

Current Art and Research Gaps (1) Social networks do influence voting in elections 1 2 Network structure can be ignored in many contexts 3 Opinions are divided 1 Sheingold, C. A. 1973. Social networks and voting: the resurrection of a research agenda. American Sociological Review 712-720. 2 Burstein, P. 1976. Social networks and voting: Some Israeli data. Social Forces 54(4):833–847. 3 Conitzer, V. 2012. Should social network structure be taken into account in elections? Mathematical Social Sciences 64(1):100-102. Y. Narahari (IISc) Scalable Preference Aggregation in Social Networks January 16, 2014 5 / 24

Current Art and Research Gaps (2) Node selection in voting using attributes of nodes and alterna- tives without taking social network into account 4 4 Soufiani, H. A.; Parkes, D. C.; and Xia, L. 2013. Preference elicitation for general random utility models. In The Twenty-Ninth Conference on Uncertainty In Artificial Intelligence , 596-605. 5 N.R. Suri and Y. Narahari. IEEE - TASE . 2012 6 Easley, D., and Kleinberg, J. 2010. Networks, Crowds, and Markets: Reasoning About a Highly Connected World . Cambridge University Press. Y. Narahari (IISc) Scalable Preference Aggregation in Social Networks January 16, 2014 6 / 24

Current Art and Research Gaps (2) Node selection in voting using attributes of nodes and alterna- tives without taking social network into account 4 Node selection in influence maximization, influence limitation, virus inoculation, etc. taking social network into account 5 6 4 Soufiani, H. A.; Parkes, D. C.; and Xia, L. 2013. Preference elicitation for general random utility models. In The Twenty-Ninth Conference on Uncertainty In Artificial Intelligence , 596-605. 5 N.R. Suri and Y. Narahari. IEEE - TASE . 2012 6 Easley, D., and Kleinberg, J. 2010. Networks, Crowds, and Markets: Reasoning About a Highly Connected World . Cambridge University Press. Y. Narahari (IISc) Scalable Preference Aggregation in Social Networks January 16, 2014 6 / 24