Cycles in synchronous iterative voting: general robustness and examples in Approval Voting

We consider synchronous iterative voting, where voters are given the opportunity to strategically choose their ballots depending on outcome deduced from previous collective choices. propose two settings for one of classical flavor with a discrete space states, and more general continuous-space setting extending first one. give robustness result cycles not relying tie-breaking rule, showing that they persist under small enough perturbations behavior voters. Then we examples in Approval Voting electorates applying simple, sincere consistent heuristics (namely Laslier’s Leader Rule or modification it) leading bad outcomes, either electing an existing Condorcet winner, possibly candidate ranked last by majority Using result, it follows those “bad cycles” even if only (large enough) fraction electorate updates its choice ballot at each iteration. complete these results other voting methods, including ranking methods satisfying criterion; silico experimental study rarity preference profiles exhibiting cycles; example chaotic behavior.