Related papers: Utilitarian Distortion Under Probabilistic Voting
The Plackett--Luce model has been extensively used for rank aggregation in social choice theory. A central statistical question in this model concerns estimating the utility vector that governs the model's likelihood. In this paper, we…
Politics around the world exhibits increasing polarization, demonstrated in part by rigid voting configurations in institutions like legislatures or courts. A crux of polarization is separation along a unidimensional ideological axis, but…
Aggregating the preferences of individuals into a collective decision is the core subject of study of social choice theory. In 2006, Procaccia and Rosenschein considered a utilitarian social choice setting, where the agents have explicit…
We consider the following well-studied problem of metric distortion in social choice. Suppose we have an election with $n$ voters and $m$ candidates located in a shared metric space. We would like to design a voting rule that chooses a…
There is a class of models for pol/mil/econ bargaining and conflict that is loosely based on the Median Voter Theorem which has been used with great success for about 30 years. However, there are fundamental mathematical limitations to…
We study social choice mechanisms in an implicit utilitarian framework with a metric constraint, where the goal is to minimize \textit{Distortion}, the worst case social cost of an ordinal mechanism relative to underlying cardinal…
By classic results in social choice theory, any reasonable preferential voting method sometimes gives individuals an incentive to report an insincere preference. The extent to which different voting methods are more or less resistant to…
In this paper, we establish a mathematical duality between utility transforms and probability distortions. These transforms play a central role in decision under risk by forming the foundation for the classic theories of expected utility,…
The traditional axiomatic approach to voting is motivated by the problem of reconciling differences in subjective preferences. In contrast, a dominant line of work in the theory of voting over the past 15 years has considered a different…
The classical paradox of social choice theory asserts that there is no fair way to deterministically select a winner in an election among more than two candidates; the only definite collective preferences are between individual pairs of…
Let $V$ be a set of $n$ points in $\mathbb{R}^d$, called voters. A point $p\in \mathbb{R}^d$ is a plurality point for $V$ when the following holds: for every $q\in\mathbb{R}^d$ the number of voters closer to $p$ than to $q$ is at least the…
In the metric distortion problem there is a set of candidates $C$ and voters $V$ in the same metric space. The goal is to select a candidate minimizing the social cost: the sum of distances of the selected candidate from all the voters, and…
The standard voting methods in the United States, plurality and ranked choice (or instant runoff) voting, are susceptible to significant voting failures. These flaws include Condorcet and majority failures as well as monotonicity and…
By the Gibbard--Satterthwaite theorem, every reasonable voting rule for three or more alternatives is susceptible to manipulation: there exist elections where one or more voters can change the election outcome in their favour by…
We introduce the notion of {\em Distance Restricted Manipulation}, where colluding manipulator(s) need to compute if there exist votes which make their preferred alternative win the election when their knowledge about the others' votes is a…
The well-known Condorcet Jury Theorem states that, under majority rule, the better of two alternatives is chosen with probability approaching one as the population grows. We study an asymmetric setting where voters face varying…
Winner selection by majority, in an election between two candidates, is the only rule compatible with democratic principles. Instead, when the candidates are three or more and the voters rank candidates in order of preference, there are no…
The Borda voting rule is a positional scoring rule for $z$ candidates such that in each vote, the first candidate receives $z-1$ points, the second $z-2$ points and so on. The winner in the Borda rule is the candidate with highest total…
Political polarization can be beneficial to competing political parties. I study how electoral competition itself generates incentives to polarize voters, even when parties are ex ante identical and motivated purely by political power,…
We study deliberative social choice, where voters engage in small-group discussions to output collective preferences that are then aggregated by a social choice rule. We introduce a simple deliberation-via-matching protocol. In this…