4,510 research outputs found
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
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
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
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
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
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