Related papers: Approval-Based Elections and Distortion of Voting …
We study the problem of minimizing metric distortion in multi-winner elections, where a committee of size $k$ is selected from a set of candidates based on voters' ordinal preferences. We assume that voters and candidates are embedded on a…
We study the following metric distortion problem: there are two finite sets of points, $V$ and $C$, that lie in the same metric space, and our goal is to choose a point in $C$ whose total distance from the points in $V$ is as small as…
We study the problem of designing voting rules that take as input the ordinal preferences of $n$ agents over a set of $m$ alternatives and output a single alternative, aiming to optimize the overall happiness of the agents. The input to the…
In Spatial Voting Theory, distortion is a measure of how good the winner is. It is proved that no deterministic voting mechanism can guarantee a distortion better than $3$, even for simple metrics such as a line. In this study, we wish to…
In computational social choice, the distortion of a voting rule quantifies the degree to which the rule overcomes limited preference information to select a socially desirable outcome. This concept has been investigated extensively, but…
In this note, we uncover three connections between the metric distortion problem and voting methods and axioms from the social choice literature.
In the well-studied metric distortion problem in social choice, we have voters and candidates located in a shared metric space, and the objective is to design a voting rule that selects a candidate with minimal total distance to the voters.…
We study the performance of voting mechanisms from a utilitarian standpoint, under the recently introduced framework of metric-distortion, offering new insights along three main lines. First, if $d$ represents the doubling dimension of 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…
In this paper, we study the distortion bounds for voting mechanisms in multi-winner elections in general metric spaces. Our study pertains to the case in which each voter only reports her favorite candidate amongst $m$ possible choices.…
Approval voting is a common method of preference aggregation where voters vote by ``approving'' of a subset of candidates and the winner(s) are those who are approved of by the largest number of voters. In approval voting, the degree to…
In this work we study the metric distortion problem in voting theory under a limited amount of ordinal information. Our primary contribution is threefold. First, we consider mechanisms which perform a sequence of pairwise comparisons…
We study social choice rules under the utilitarian distortion framework, with an additional metric assumption on the agents' costs over the alternatives. In this approach, these costs are given by an underlying metric on the set of all…
We consider models for social choice where voters rank a set of choices (or alternatives) by deliberating in small groups of size at most $k$, and these outcomes are aggregated by a social choice rule to find the winning alternative. We…
We consider a social choice setting in which agents and alternatives are represented by points in a metric space, and the cost of an agent for an alternative is the distance between the corresponding points in the space. The goal is to…
{\em Distortion} is a well-established notion for quantifying the loss of social welfare that may occur in voting. As voting rules take as input only ordinal information, they are essentially forced to neglect the exact values the agents…
We consider a distributed voting problem with a set of agents that are partitioned into disjoint groups and a set of obnoxious alternatives. Agents and alternatives are represented by points in a metric space. The goal is to compute the…
In voting with ranked ballots, each agent submits a strict ranking of the form $a \succ b \succ c \succ d$ over the alternatives, and the voting rule decides on the winner based on these rankings. Although this ballot format has desirable…
We consider a setting with agents that have preferences over alternatives and are partitioned into disjoint districts. The goal is to choose one alternative as the winner using a mechanism which first decides a representative alternative…
Consider the following social choice problem. Suppose we have a set of $n$ voters and $m$ candidates that lie in a metric space. The goal is to design a mechanism to choose a candidate whose average distance to the voters is as small as…