Possible and necessary winner problem in social polls

Authors:
Serge Gaspers;Victor Naroditskiy;Nina Narodytska;Toby Walsh
Affiliations:
The University of New South Wales and NICTA, Sydney, Australia, Australia;University of Southampton, Southampton, United Kingdom;NICTA and The University of New South Wales, Sydney, Australia;NICTA and The University of New South Wales, Sydney, Australia
Venue:
Proceedings of the 2013 international conference on Autonomous agents and multi-agent systems
Year:
2013

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Abstract

Social networks are increasingly being used to conduct polls. We introduce a simple model of such social polling. We suppose agents vote sequentially, but the order in which agents choose to vote is not necessarily fixed. We also suppose that an agent's vote is influenced by the votes of their friends who have already voted. Despite its simplicity, this model provides useful insights into a number of areas including social polling, sequential voting, and manipulation. We prove that the number of candidates and the network structure affect the computational complexity of computing which candidate necessarily or possibly can win in such a social poll. For social networks with bounded treewidth and a bounded number of candidates, we provide polynomial algorithms for both problems. In other cases, we prove that computing which candidates necessarily or possibly win are computationally intractable.