SAGT 2016: Algorithmic Game Theory pp 182-194

# Strong and Weak Acyclicity in Iterative Voting

• Reshef Meir
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9928)

## Abstract

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 (the response played by the agent).

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 [17]. In addition, we refute another conjecture by showing the existence of strongly-acyclic voting rules that are not separable.

## Keywords

Nash Equilibrium Vote Rule Game Form Preference Profile Plurality Rule
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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