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

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

On the Actual Inefficiency of Efficient Negotiation Methods

In this contribution we analyze the effect that mutual information has on the actual performance of efficient negotiation methods. Specifically, we start by proposing the theoretical notion of Abstract Negotiation Method (ANM) as a map from the negotiation domain in itself, for any utility profile of the parties. ANM can face both direct and iterative negotiations, since we show that ANM class is closed under the limit operation. The generality of ANM is proven by showing that it captures a large class of well known in literature negotiation methods. Hence we show that if mutual information is assumed then any Pareto efficient ANM is manipulable by one single party or by a collusion of few of them. We concern about the efficiency of the resulting manipulation. Thus we find necessarily and sufficient conditions those make manipulability equivalent to actual inefficiency, meaning that the manipulation implies a change of the efficient frontier so the Pareto efficient ANM converges to a different, hence actually inefficient, frontier. In particular we distinguish between strong and weak actual inefficiency. Where, the strong actual inefficiency is a drawback which is not possible to overcome of the ANMs, like the Pareto invariant one, so its negotiation result is invariant for any two profiles of utility sharing the same Pareto frontier, we present. While the weak actual inefficiency is a drawback of any mathematical theorization on rational agents which constrain in a particular way their space of utility functions. For the weak actual inefficiency we state a principle of Result's Inconsistency by showing that to falsify theoretical hypotheses is rational for any agent which is informed about the preference of the other, even if the theoretical assumptions, which constrain the space of agents' utilities, are exact in the reality, i.e. the preferences of each single agent are well modeled

Strategic Behavior is Bliss: Iterative Voting Improves Social Welfare

Recent work in iterative voting has defined the additive dynamic price of anarchy (ADPoA) as the difference in social welfare between the truthful and worst-case equilibrium profiles resulting from repeated strategic manipulations. While iterative plurality has been shown to only return alternatives with at most one less initial votes than the truthful winner, it is less understood how agents' welfare changes in equilibrium. To this end, we differentiate agents' utility from their manipulation mechanism and determine iterative plurality's ADPoA in the worst- and average-cases. We first prove that the worst-case ADPoA is linear in the number of agents. To overcome this negative result, we study the average-case ADPoA and prove that equilibrium winners have a constant order welfare advantage over the truthful winner in expectation. Our positive results illustrate the prospect for social welfare to increase due to strategic manipulation.Comment: 21 pages, 5 figures, in NeurIPS 202

A Local-Dominance Theory of Voting Equilibria

It is well known that no reasonable voting rule is strategyproof. Moreover, the common Plurality rule is particularly prone to strategic behavior of the voters and empirical studies show that people often vote strategically in practice. Multiple game-theoretic models have been proposed to better understand and predict such behavior and the outcomes it induces. However, these models often make unrealistic assumptions regarding voters' behavior and the information on which they base their vote. We suggest a new model for strategic voting that takes into account voters' bounded rationality, as well as their limited access to reliable information. We introduce a simple behavioral heuristic based on \emph{local dominance}, where each voter considers a set of possible world states without assigning probabilities to them. This set is constructed based on prospective candidates' scores (e.g., available from an inaccurate poll). In a \emph{voting equilibrium}, all voters vote for candidates not dominated within the set of possible states. We prove that these voting equilibria exist in the Plurality rule for a broad class of local dominance relations (that is, different ways to decide which states are possible). Furthermore, we show that in an iterative setting where voters may repeatedly change their vote, local dominance-based dynamics quickly converge to an equilibrium if voters start from the truthful state. Weaker convergence guarantees in more general settings are also provided. Using extensive simulations of strategic voting on generated and real preference profiles, we show that convergence is fast and robust, that emerging equilibria are consistent across various starting conditions, and that they replicate widely known patterns of human voting behavior such as Duverger's law. Further, strategic voting generally improves the quality of the winner compared to truthful voting