Average-Case Analysis of Iterative Voting

It is well-known in social choice that people may misreport their preferences to improve group decisions in their favor. Consider, for example, Alice, Bob, and Charlie deciding on which ice cream flavor to order for a party, and Charlie prefers strawberry to chocolate to vanilla. Given that Alice wants chocolate and Bob wants vanilla, Charlie would be better off voting for chocolate than truthfully (i.e., strawberry), by which vanilla may win as the tie-breaker. This form of strategic behavior is prolific in political science in narrowing the number of political parties (see e.g., Duvuger's law [Riker, 1982]). Still, it is unclear what effect strategic behavior has on the social welfare of chosen outcomes. Iterative voting (IV) is one model which naturally describes agents' strategic behavior - in misreporting their truthful preferences - over time. After agents reveal their preferences initially, they have the opportunity to repeatedly update their votes given information about other agents' votes, before the final decision is reached. Meir et al. [2010] first proposed iterative plurality voting and identified many sufficient conditions for IV to converge. This was followed up by a series of work examining various social choice rules, information and behavioral assumptions, and settings to determine when, to what outcomes, and how fast IV converges (see e.g.