Approval Voting in Product Societies

@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… 
Piercing Numbers in Circular Societies
. 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
Approval Voting in Circular Societies: Piercing Numbers and Agreement
TLDR
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.
Piercing numbers in approval voting

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MUTIARA SONDJAJA received her Ph.D. in 2014 from the School of Operations Research and Information