Convergence of Iterative Voting Under Restrictive Dynamics for Plurality Rule: A Review

Abstract

In multi-agent systems, social choice can help aggregate the distinct preferences that agents have over alternatives, enabling them to settle on a single choice. Despite the basic manipulability of all reasonable voting systems, it would still be desirable to find ways to reach plausible outcomes, which are stable states, i.e., a situation where no agent would wish to change its vote. Iterative voting is one way in which, after everyone initially votes, voters may change their votes, one voter at a time. This technique, explored in previous work, converges to a Nash equilibrium when Plurality voting is used, along with a tie-breaking rule i.e., lexicographic rule. There are many turns in the game, where a single voter at each turn can change his vote and the final outcome is announced when no voter has objections. In this paper, we are reviewing and analyzing the results of convergence of iterative voting under restrictive dynamics for plurality rule. We categorized convergence based on different strategies, these strategies are best reply dynamics, potential functions, weighted voters, truth biased and the role of tie breaking rules. We reviewed the literature that convergence is guaranteed dependent on the above mentioned restrictions. We also added some open questions; our work would be helpful in providing literature to some of those questions.