@article{Mazur2018ApprovalVI,
title={Approval Voting in Product Societies},
author={Kristen Mazur and Mutiara Sondjaja and Matthew L. Wright and Carolyn Yarnall},
journal={The American Mathematical Monthly},
year={2018},
volume={125},
pages={29 - 43}
}

Abstract In approval voting, individuals vote for all platforms that they find acceptable. In this situation it is natural to ask: When is agreement possible? What conditions guarantee that some fraction of the voters agree on even a single platform? Berg et al. found such conditions when voters are asked to make a decision on a single issue that can be represented on a linear spectrum. In particular, they showed that if two out of every three voters agree on a platform, there is a platform… Expand

. In the system of approval voting, individuals vote for all candidates they ﬁnd acceptable. Many approval voting situations can be modeled geometrically, and thus geometric concepts such as the… Expand

This paper explores piercing numbers and agreement in the setting where preferences can be modeled by arcs on a circle -- i.e., in circular societies with fixed-length approval sets, and gives bounds on piercing and agreement.Expand

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… Expand

Examples of situations where sets model preferences and develop extensions of classical theorems about convex sets that can be used in the analysis of voting in "agreeable" societies are given.Expand

The Supreme Court of the United States has held that bizarrely shaped congressional districts threaten the equal voting rights of U.S. citizens. Attempting to quantify this bizarreness, myriad… Expand