TY - UNPB
T1 - Plurality in Spatial Voting Games with constant $β$.
AU - Filtser, Arnold
AU - Filtser, Omrit
N1 - DBLP's bibliographic metadata records provided through http://dblp.org/search/publ/api are distributed under a Creative Commons CC0 1.0 Universal Public Domain Dedication. Although the bibliographic metadata records are provided consistent with CC0 1.0 Dedication, the content described by the metadata records is not. Content may be subject to copyright, rights of privacy, rights of publicity and other restrictions.
PY - 2020
Y1 - 2020
N2 - Consider a set V of voters, represented by a multiset in a metric space (X,d). The voters have to reach a decision -- a point in X. A choice p∈X is called a β-plurality point for V, if for any other choice q∈X it holds that |{v∈V∣β⋅d(p,v)≤d(q,v)}|≥|V|2. In other words, at least half of the voters ``prefer'' p over q, when an extra factor of β is taken in favor of p. For β=1, this is equivalent to Condorcet winner, which rarely exists. The concept of β-plurality was suggested by Aronov, de Berg, Gudmundsson, and Horton [TALG 2021] as a relaxation of the Condorcet criterion.Let β∗(X,d)=sup{β∣every finite multiset V in X admits a β-plurality point}. The parameter β∗ determines the amount of relaxation required in order to reach a stable decision. Aronov et al. showed that for the Euclidean plane β∗(R2,∥⋅∥2)=3√2, and more generally, for d-dimensional Euclidean space, 1d√≤β∗(Rd,∥⋅∥2)≤3√2. In this paper, we show that 0.557≤β∗(Rd,∥⋅∥2) for any dimension d (notice that 1d√<0.557 for any d≥4). In addition, we prove that for every metric space (X,d) it holds that 2–√−1≤β∗(X,d), and show that there exists a metric space for which β∗(X,d)≤12.
AB - Consider a set V of voters, represented by a multiset in a metric space (X,d). The voters have to reach a decision -- a point in X. A choice p∈X is called a β-plurality point for V, if for any other choice q∈X it holds that |{v∈V∣β⋅d(p,v)≤d(q,v)}|≥|V|2. In other words, at least half of the voters ``prefer'' p over q, when an extra factor of β is taken in favor of p. For β=1, this is equivalent to Condorcet winner, which rarely exists. The concept of β-plurality was suggested by Aronov, de Berg, Gudmundsson, and Horton [TALG 2021] as a relaxation of the Condorcet criterion.Let β∗(X,d)=sup{β∣every finite multiset V in X admits a β-plurality point}. The parameter β∗ determines the amount of relaxation required in order to reach a stable decision. Aronov et al. showed that for the Euclidean plane β∗(R2,∥⋅∥2)=3√2, and more generally, for d-dimensional Euclidean space, 1d√≤β∗(Rd,∥⋅∥2)≤3√2. In this paper, we show that 0.557≤β∗(Rd,∥⋅∥2) for any dimension d (notice that 1d√<0.557 for any d≥4). In addition, we prove that for every metric space (X,d) it holds that 2–√−1≤β∗(X,d), and show that there exists a metric space for which β∗(X,d)≤12.
U2 - 10.48550/arXiv.2005.04799
DO - 10.48550/arXiv.2005.04799
M3 - פרסום מוקדם
VL - abs/2005.04799
BT - Plurality in Spatial Voting Games with constant $β$.
ER -