We consider best-reply dynamics for voting games in which all players are strategic and no coalitions are formed. We study the class of scoring rules, show convergence of a suitably restricted version for the plurality and veto rules, and failure of convergence for other rules including κ-approval and Borda. In particular, for 3 candidates convergence fails for all rules other than plurality and veto. We give a unified proof for the convergence of these two rules. Our proofs in the case of plurality improve the known bound on convergence, and the other convergence results are new.
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