2013/07/18 by Maria Klawe, Kathryn Nyman, Kathryn L. Nyman +6
Economics, Econometrics and Finance · Mathematics · Social Sciences · #52A35 #91B12 #Combinatorics #Combinatorics (math.CO) #Computer science #Disjoint sets #Electoral Systems and Political Participation #FOS: Mathematics #Game Theory and Voting Systems #Geography #Intersection (aeronautics) #Interval (graph theory) #Law #Mathematical economics #Mathematics #Media Influence and Politics #Pairwise comparison #Point (geometry) #Political science #Politics #Popularity #Set (abstract data type) #Statistics #Symbol (formal) #Upper and lower bounds #math.CO #msc:52A35 #msc:91B12
paper · pdf · doi:10.48550/arxiv.1307.5094
12 pages, 6 figures
arxiv created 2013/07/18 · openalex publication_date 2013/07/18 · arxiv updated 2013/07/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
Consider a society of voters, each of whom specify an approval set over a linear political spectrum. We examine double-interval societies, in which each person's approval set is represented by two disjoint closed intervals, and study this situation where the approval sets are pairwise-intersecting: every pair of voters has a point in the intersection of their approval sets. The approval ratio for a society is, loosely speaking, the popularity of the most popular position on the spectrum. We study the question: what is the minimal guaranteed approval ratio for such a society? We provide a lower bound for the approval ratio, and examine a family of societies that have rather low approval ratios. These societies arise from double-n strings: arrangements of n symbols in which each symbol appears exactly twice.