Double-interval societies
Abstract
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.
Cite
@article{arxiv.1307.5094,
title = {Double-interval societies},
author = {Maria Klawe and Kathryn L. Nyman and Jacob N. Scott and Francis Edward Su},
journal= {arXiv preprint arXiv:1307.5094},
year = {2013}
}
Comments
12 pages, 6 figures