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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 Lasliers 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 voters 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.
Justified representation (JR) is a standard notion of representation in multiwinner approval voting. Not only does a JR committee always exist, but previous work has also shown through experiments that the JR condition can typically be fulfilled by g
We study sincere-strategy preference-based approval voting (SP-AV), a system proposed by Brams and Sanver [Electoral Studies, 25(2):287-305, 2006], and here adjusted so as to coerce admissibility of the votes (rather than excluding inadmissible votes
Shortlisting is the task of reducing a long list of alternatives to a (smaller) set of best or most suitable alternatives from which a final winner will be chosen. Shortlisting is often used in the nomination process of awards or in recommender syste
Gradient descent is arguably one of the most popular online optimization methods with a wide array of applications. However, the standard implementation where agents simultaneously update their strategies yields several undesirable properties; strate
We analyse strategic, complete information, sequential voting with ordinal preferences over the alternatives. We consider several voting mechanisms: plurality voting and approval voting with deterministic or uniform tie-breaking rules. We show that s