Year: 2020
Type: preprint
Abstract: 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 number of voters closer to $q$ than to $p$. Thus, in a vote where each $v\in V$ votes for the nearest proposal (and voters for which the proposals are at equal distance abstain), proposal $p$ will not lose against any alternative proposal $q$. For most voter sets a plurality point does not exist. We therefore introduce the concept of $β$-plurality points, which are defined similarly to regular plurality points except that the distance of each voter to $p$ (but not to $q$) is scaled by a factor $β$, for some constant $0
Source: arXiv (Cornell University)
Authors: Aronov, Boris, de Berg, Mark, Gudmundsson, Joachim, Horton, Michael
Language: English
Subfield: Economics and Econometrics
Domain: Social Sciences
Open Access status: green
Awards: G4569202905, G565383568
OpenAlex ID: W3010691183