12,331 research outputs found
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
Are Condorcet and minimax voting systems the best?
For decades, the minimax voting system was well known to experts on voting
systems, but was not widely considered to be one of the best systems. But in
recent years, two important experts, Nicolaus Tideman and Andrew Myers, have
both recognized minimax as one of the best systems. I agree with that. This
paper presents my own reasons for preferring minimax. The paper explicitly
discusses about 20 systems, though over 50 are known to exist.Comment: 41 pages, no figures. The Introduction has been changed. Also fixed
some version 6 errors in referencing subsection numbers in section
Sincere Scoring Rules
Approval Voting is shown to be the unique scoring rule that leads strategic voters to sincere behavior of three candidates elections in Poisson Games. However, Approval Voting can lead to insincere behavior in elections with more than three candidates.Sincerity, Approval Voting, Scoring rules, Poisson Games
The basic approval voting game
We survey results about Approval Voting obtained within the standard framework of game theory. Restricting the set of strategies to undominated and sincere ballots does not help to predict Approval Voting outcomes, which is also the case under strategic equilibrium concepts such as Nash equilibrium and its usual refinements. Strong Nash equilibrium in general does not exist but predicts the election of a Condorcet winner when one exists
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
Strategic, Sincere and Heuristic Voting under Four Election Rules: An Experimental Study
We report on laboratory experiments on voting. In a setting where subjects have single-peaked preferences we find that the rational choice theory provides very good predictions of actual individual behavior in one-round and approval voting elections, but fares poorly in explaining vote choice under two-round elections. We conclude that voters behave strategically as far as strategic computations are not too demanding, in which case they rely on simple heuristics (in two-round elections) or they just vote sincerely (in single transferable vote elections).
Laboratory Experiments in Political Economy
Most of the laboratory research in political science follows the style that was pioneered in experimental economics a half-century ago by Vernon Smith. The connection between this style of political science experimentation and economics experimentation parallels the connection between economic theory and formal political theory.
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