Related papers: Plurality in Spatial Voting Games with constant $\…
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…
We initiate the work towards a comprehensive picture of the smoothed satisfaction of voting axioms, to provide a finer and more realistic foundation for comparing voting rules. We adopt the smoothed social choice framework, where an…
In this note we consider situations of (multidimensional) spatial majority voting. We show that under some assumptions usual in this literature, with an even number of voters if the core of the voting situation is singleton (and in the…
We consider a spatial voting model where both candidates and voters are positioned in the $d$-dimensional Euclidean space, and each voter ranks candidates based on their proximity to the voter's ideal point. We focus on the scenario where…
We give conditions for equilibria in the following Voronoi game on the discrete hypercube. Two players position themselves in $\{0,1\}^d$ and each receives payoff equal to the measure (under some probability distribution) of their Voronoi…
We show that the proportional clustering problem using the Droop quota for $k = 1$ is equivalent to the $\beta$-plurality problem. We also show that the Plurality Veto rule can be used to select ($\sqrt{5} - 2$)-plurality points using only…
The utilitarian distortion framework evaluates voting rules by their worst-case efficiency loss when voters have cardinal utilities but express only ordinal rankings. Under the classical model, a longstanding tension exists: Plurality,…
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…
Typical voting rules do not work well in settings with many candidates. If there are just several hundred candidates, then even a simple task such as choosing a top candidate becomes impractical. Motivated by the hope of developing group…
Plurality and approval voting are two well-known voting systems with different strengths and weaknesses. In this paper we consider a new voting system we call beta(k) which allows voters to select a single first-choice candidate and approve…
Understanding the nature of strategic voting is the holy grail of social choice theory, where game-theory, social science and recently computational approaches are all applied in order to model the incentives and behavior of voters. In a…
Metric distortion in social choice is a framework for evaluating how well voting rules minimize social cost when both voters and candidates exist in a shared metric space, with a voter's cost defined by their distance to a candidate. Voters…
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…
Given a finite set $S$ of points in $\mathbb{R}^d$, which we regard as the locations of voters on a $d$-dimensional political `spectrum', two candidates (Alice and Bob) select one point in $\mathbb{R}^d$ each, in an attempt to get as many…
Classical spatial models of two-party competition typically predict convergence to the median voter, yet real-world party systems often exhibit persistent and asymmetric polarization. We develop a spatial model of two-party competition in…
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…
A Condorcet winning set is a set of candidates such that no other candidate is preferred by at least half the voters over all members of the set. The Condorcet dimension, which is the minimum cardinality of a Condorcet winning set, is known…
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…
We study the probability that a given candidate is an alpha-winner, i.e. a candidate preferred to each other candidate j by a fraction alpha_j of the voters. This extends the classical notion of Condorcet winner, which corresponds to the…
A Condorcet winning set addresses the Condorcet paradox by selecting a few candidates--rather than a single winner--such that no unselected alternative is preferred to all of them by a majority of voters. This idea extends to…