Strong and Weak Acyclicity in Iterative Voting

We cast the various different models used for the analysis of iterative voting schemes into a general framework, consistent with the literature on acyclicity in games. More specifically, we classify convergence results based on the underlying assumptions on the agent scheduler (the order of players) and the action scheduler (which better-reply is played). Our main technical result is proving that Plurality with randomized tie-breaking (which is not guaranteed to converge under arbitrary agent schedulers) is weakly-acyclic. I.e., from any initial state there is some path of better-replies to a Nash equilibrium. We thus show a separation between restricted-acyclicity and weak-acyclicity of game forms, thereby settling an open question from [18].