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This paper introduces a novel binary stability property for voting rules-called binary self-selectivity-by which a society considering whether to replace its voting rule using itself in pairwise elections will choose not to do so. In…
In perpetual voting, multiple decisions are made at different moments in time. Taking the history of previous decisions into account allows us to satisfy properties such as proportionality over periods of time. In this paper, we consider…
Condorcet winning sets are a set-valued generalization of the well-known concept of a Condorcet winner. As supersets of Condorcet winning sets are always Condorcet winning sets themselves, an interesting property of preference profiles is…
We consider voting on multiple independent binary issues. In addition, a weighting vector for each voter defines how important they consider each issue. The most natural way to aggregate the votes into a single unified proposal is…
We study computational aspects of three prominent voting rules that use approval ballots to elect multiple winners. These rules are satisfaction approval voting, proportional approval voting, and reweighted approval voting. We first show…
We study two notions of stability in multiwinner elections that are based on the Condorcet criterion. The first notion was introduced by Gehrlein: A committee is stable if each committee member is preferred to each non-member by a (possibly…
The main idea of the {\em distance rationalizability} approach to view the voters' preferences as an imperfect approximation to some kind of consensus is deeply rooted in social choice literature. It allows one to define ("rationalize")…
We consider synchronous iterative voting, where voters are given the opportunity to strategically choose their ballots depending on the outcome deduced from the previous collective choices.We propose two settings for synchronous iterative…
The metric distortion framework posits that n voters and m candidates are jointly embedded in a metric space such that voters rank candidates that are closer to them higher. A voting rule's purpose is to pick a candidate with minimum total…
We revisit the recent breakthrough result of Gkatzelis et al. on (single-winner) metric voting, which showed that the optimal distortion of 3 can be achieved by a mechanism called Plurality Matching. The rule picks an arbitrary candidate…
Condorcet domains are subsets of permutations arising in voting theory: regarding their permutations as preference orders on a list of candidates, one avoids Condorcet's paradox when aggregating the preferences via a simple majority…
The important Kemeny problem, which consists of computing median consensus rankings of an election with respect to the Kemeny voting rule, admits important applications in biology and computational social choice and was generalized recently…
We propose a new single-winner election method ("Schulze method") and prove that it satisfies many academic criteria (e.g. monotonicity, reversal symmetry, resolvability, independence of clones, Condorcet criterion, k-consistency,…
The voting systems known as Alternative Vote (AV) and Single Transferable Vote (STV) are extensively used for elections in Australia, possibly more than in any other jurisdiction. Often proposed as superior alternatives to Plurality and…
May's Theorem [K. O. May, Econometrica 20 (1952) 680-684] characterizes majority voting on two alternatives as the unique preferential voting method satisfying several simple axioms. Here we show that by adding some desirable axioms to…
We investigate the collective accuracy of heterogeneous agents who learn to estimate their own reliability over time and selectively abstain from voting. While classical epistemic voting results, such as the \textit{Condorcet Jury Theorem}…
We propose a Condorcet consistent voting method that we call Split Cycle. Split Cycle belongs to the small family of known voting methods satisfying the anti-vote-splitting criterion of independence of clones. In this family, only Split…
An important aspect of AI design and ethics is to create systems that reflect aggregate preferences of the society. To this end, the techniques of social choice theory are often utilized. We propose a new social choice function motivated by…
We present a simple proof of a well-known axiomatic characterization of state-salient decision rules, using Weak Dominance Criterion and Global Independence of Irrelevant Alternatives. Subsequently we provide a simple axiomatic…
Several of the classical results in social choice theory demonstrate that in order for many voting systems to be well-behaved the set domain of individual preferences must satisfy some kind of restriction, such as being single-peaked on a…