1,238 research outputs found
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
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 convergence of iterative voting: how restrictive should restricted dynamics be?
We study convergence properties of iterative voting procedures. Such procedures are defined by a voting rule and a (restricted) iterative process, where at each step one agent can modify his vote towards a better outcome for himself. It is already known that if the iteration dynamics (the manner in which voters are allowed to modify their votes) are unrestricted, then the voting process may not converge. For most common voting rules this may be observed even under the best response dynamics limitation. It is therefore important to investigate whether and which natural restrictions on the dynamics of iterative voting procedures can guarantee convergence. To this end, we provide two general conditions on the dynamics based on iterative myopic improvements, each of which is sufficient for convergence. We then identify several classes of voting rules (including Positional Scoring Rules, Maximin, Copeland and Bucklin), along with their corresponding iterative processes, for which at least one of these conditions hold
Combinatorial Voting
We study elections that simultaneously decide multiple issues, where voters have independent private values over bundles of issues. The innovation is in considering nonseparable preferences, where issues may be complements or substitutes. Voters face a political exposure problem: the optimal vote for a particular issue will depend on the resolution of the other issues. Moreover, the probabilities that the other issues will pass should be conditioned on being pivotal. We prove that equilibrium exists when distributions over values have full support or when issues are complements. We then study large elections with two issues. There exists a nonempty open set of distributions where the probability of either issue passing fails to converge to either 1 or 0 for all limit equilibria. Thus, the outcomes of large elections are not generically predictable with independent private values, despite the fact that there is no aggregate uncertainty regarding fundamentals. While the Condorcet winner is not necessarily the outcome of a multi-issue election, we provide sufficient conditions that guarantee the implementation of the Condorcet winner. © 2012 The Econometric Society
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
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