Plurality Voting under Uncertainty

Understanding the nature of strategic voting is the holy grail of social choice theory, where game-theory, social science and recently computational approaches are all applied in order to model the incentives and behavior of voters. In a recent paper, Meir et al.[EC'14] made another step in this direction, by suggesting a behavioral game-theoretic model for voters under uncertainty. For a specific variation of best-response heuristics, they proved initial existence and convergence results in the Plurality voting system. In this paper, we extend the model in multiple directions, considering voters with different uncertainty levels, simultaneous strategic decisions, and a more permissive notion of best-response. We prove that a voting equilibrium exists even in the most general case. Further, any society voting in an iterative setting is guaranteed to converge. We also analyze an alternative behavior where voters try to minimize their worst-case regret. We show that the two behaviors coincide in the simple setting of Meir et al., but not in the general case.Comment: The full version of a paper from AAAI'15 (to appear

Reaching Consensus Under a Deadline

Committee decisions are complicated by a deadline, e.g., the next start of a budget, or the beginning of a semester. In committee hiring decisions, it may be that if no candidate is supported by a strong majority, the default is to hire no one - an option that may cost dearly. As a result, committee members might prefer to agree on a reasonable, if not necessarily the best, candidate, to avoid unfilled positions. In this paper, we propose a model for the above scenario - Consensus Under a Deadline (CUD)- based on a time-bounded iterative voting process. We provide convergence guarantees and an analysis of the quality of the final decision. An extensive experimental study demonstrates more subtle features of CUDs, e.g., the difference between two simple types of committee member behavior, lazy vs.~proactive voters. Finally, a user study examines the differences between the behavior of rational voting bots and real voters, concluding that it may often be best to have bots play on the voters' behalf

Acyclic Games and Iterative Voting

We consider iterative voting models and position them within the general framework of acyclic games and game forms. 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 providing a complete picture of conditions for acyclicity in several variations of Plurality voting. In particular, we show that (a) under the traditional lexicographic tie-breaking, the game converges for any order of players under a weak restriction on 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 \emph{some} path of better-replies to a Nash equilibrium. We thus show a first separation between restricted-acyclicity and weak-acyclicity of game forms, thereby settling an open question from [Kukushkin, IJGT 2011]. In addition, we refute another conjecture regarding strongly-acyclic voting rules.Comment: some of the results appeared in preliminary versions of this paper: Convergence to Equilibrium of Plurality Voting, Meir et al., AAAI 2010; Strong and Weak Acyclicity in Iterative Voting, Meir, COMSOC 201

Bad cycles in iterative Approval Voting

This article is about synchronized iterative voting in the context of Approval Voting. Assuming that, before an election, successive polls occur to which voters react strategically, we shall exhibit examples showing the possibility of cycles with strong negative properties (in particular, non election of an existing Condorcet winner, or possible election of a candidate strongly rejected by a majority of the electorate). We also show that such cycles persist if only a proportion of the voters adjust their ballot at each iteration and if their strategy changes when close ties occur

Bad cycles and chaos in iterative Approval Voting

We consider synchronized iterative voting in the Approval Voting system. We give examples with a Condorcet winner where voters apply simple, sincere, consistent strategies but where cycles appear that can prevent the election of the Condorcet winner, or that can even lead to the election of a ''consensual loser'', rejected in all circumstances by a majority of voters. We conduct numerical experiments to determine how rare such cycles are. It turns out that when voters apply Laslier's Leader Rule they are quite uncommon, and we prove that they cannot happen when voters' preferences are modeled by a one-dimensional culture. However a slight variation of the Leader Rule accounting for possible draws in voter's preferences witnesses much more bad cycle, especially in a one-dimensional culture.Then we introduce a continuous-space model in which we show that these cycles are stable under perturbation. Last, we consider models of voters behavior featuring a competition between strategic behavior and reluctance to vote for candidates that are ranked low in their preferences. We show that in some cases, this leads to chaotic behavior, with fractal attractors and positive entropy.Comment: v2: added a numerical study of rarity of bad cycles and equilibriums, and a case of chaotic Continuous Polling Dynamics. Many other improvements throughout the tex

Convergence of Multi-Issue Iterative Voting under Uncertainty

We study the effect of strategic behavior in iterative voting for multiple issues under uncertainty. We introduce a model synthesizing simultaneous multi-issue voting with Meir, Lev, and Rosenschein (2014)'s local dominance theory and determine its convergence properties. After demonstrating that local dominance improvement dynamics may fail to converge, we present two sufficient model refinements that guarantee convergence from any initial vote profile for binary issues: constraining agents to have O-legal preferences and endowing agents with less uncertainty about issues they are modifying than others. Our empirical studies demonstrate that although cycles are common when agents have no uncertainty, introducing uncertainty makes convergence almost guaranteed in practice.Comment: 19 pages, 4 figure