Acyclic Games and Iterative Voting

We consider iterative voting models and position them withi n t e general framework of acyclic games and game forms. More specifically, we classify convergence resu lts based on the underlying assumptions on the agent scheduler (the order of players) and the action scheduler (w hich better-reply is played). Our main technical result is providing a complete picture of c nditions for acyclicity in several variations of Plurality voting. In particular, we show that (a) under th e traditional lexicographic tie-breaking, the game converges for any order of players under a weak restriction o n voters’ actions; and (b) Plurality with randomized tie-breaking is not guaranteed to converge under arbitrary agent schedulers, but from any initial state there is somepath of better-replies to a Nash equilibrium. We thus show a fi rst separation between restricted-acyclicity and weak-acyclicity of game forms, thereby settling an open question from [Kukushkin, 2011]. In addition, we refute another conjecture regarding strongly-acyclic vot ing rules.

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