Possible and Necessary Winner Problem in Social Polls
This addresses the computational challenges in analyzing social polls for researchers in social choice and network theory, though it is incremental as it builds on existing models of sequential voting and influence.
The paper tackles the problem of determining which candidates can possibly or necessarily win in social polls where agents vote sequentially under social influence, showing that computational complexity depends on network structure and candidate count. It provides polynomial-time algorithms for networks with bounded treewidth and bounded candidates, and proves intractability in other cases.
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.