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

To vote or to abstain? An experimental study or first past the poste and PR elections

We examine through an experimental design how rational and non-rational considerations affect the decision to vote or to abstain in First Past the Post and PR elections. We show that in both types of elections, but particularly so under PR, a majority of subjects do not make the "right" decision, that is, they do not choose the option that is the most beneficial to them, given. We also demonstrate that a social norm such as sense of civic duty plays a bigger role, even in the lab, and particularly so in PR elections. We suggest that civic duty has a greater impact under PR because this electoral system has a more complicated formula, making it more difficult for voters to realize that their vote is unlikely to substantially affect the outcome of the election.Experiments, Voting, First Past the Post, Proportional Representation, Civic Duty

Heuristic Voting as Ordinal Dominance Strategies

Decision making under uncertainty is a key component of many AI settings, and in particular of voting scenarios where strategic agents are trying to reach a joint decision. The common approach to handle uncertainty is by maximizing expected utility, which requires a cardinal utility function as well as detailed probabilistic information. However, often such probabilities are not easy to estimate or apply. To this end, we present a framework that allows "shades of gray" of likelihood without probabilities. Specifically, we create a hierarchy of sets of world states based on a prospective poll, with inner sets contain more likely outcomes. This hierarchy of likelihoods allows us to define what we term ordinally-dominated strategies. We use this approach to justify various known voting heuristics as bounded-rational strategies.Comment: This is the full version of paper #6080 accepted to AAAI'1

Utilitarian Collective Choice and Voting

In his seminal Social Choice and Individual Values, Kenneth Arrow stated that his theory applies to voting. Many voting theorists have been convinced that, on account of Arrow’s theorem, all voting methods must be seriously flawed. Arrow’s theory is strictly ordinal, the cardinal aggregation of preferences being explicitly rejected. In this paper I point out that all voting methods are cardinal and therefore outside the reach of Arrow’s result. Parallel to Arrow’s ordinal approach, there evolved a consistent cardinal theory of collective choice. This theory, most prominently associated with the work of Harsanyi, continued the older utilitarian tradition in a more formal style. The purpose of this paper is to show that various derivations of utilitarian SWFs can also be used to derive utilitarian voting (UV). By this I mean a voting rule that allows the voter to score each alternative in accordance with a given scale. UV-k indicates a scale with k distinct values. The general theory leaves k to be determined on pragmatic grounds. A (1,0) scale gives approval voting. I prefer the scale (1,0,-1) and refer to the resulting voting rule as evaluative voting. A conclusion of the paper is that the defects of conventional voting methods result not from Arrow’s theorem, but rather from restrictions imposed on voters’ expression of their preferences. The analysis is extended to strategic voting, utilizing a novel set of assumptions regarding voter behavior