Plurality in Spatial Voting Games with Constant β

Arnold Filtser, Omrit Filtser

פרסום מחקרי: פרסום בכתב עתמאמרביקורת עמיתים


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∣everyfinitemultisetVinXadmitsaβ-pluralitypoint} . 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)∗=32 , and more generally, for d-dimensional Euclidean space, 1d≤β(Rd,‖·‖2)∗≤32 . 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 .

שפה מקוריתאנגלית
כתב עתDiscrete and Computational Geometry
מזהי עצם דיגיטלי (DOIs)
סטטוס פרסוםהתקבל/בדפוס - 2024

הערה ביבליוגרפית

Publisher Copyright:
© 2024, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.

טביעת אצבע

להלן מוצגים תחומי המחקר של הפרסום 'Plurality in Spatial Voting Games with Constant β'. יחד הם יוצרים טביעת אצבע ייחודית.

פורמט ציטוט ביבליוגרפי