Voting in Agreeable Societies

@article{Berg2010VotingIA,
  title={Voting in Agreeable Societies},
  author={Deborah E. Berg and Serguei Norine and Francis Edward Su and Robin Thomas and Paul Wollan},
  journal={The American Mathematical Monthly},
  year={2010},
  volume={117},
  pages={27 - 39}
}
When can a majority of voters find common ground, that is, a position they all agree upon? How does the shape of the political spectrum influence the outcome? When mathematical objects have a social interpretation, the associated theorems have social applications. In this article we give examples of situations where sets model preferences and develop extensions of classical theorems about convex sets, such as Helly's theorem, that can be used in the analysis of voting in "agreeable" societies. 
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26 Citations
Highly Influential Citations
6
Background Citations
16
Methods Citations
6
Results Citations
2

26 Citations

Voter Compatibility In Interval Societies
In an interval society, voters are represented by intervals on the real line, corresponding to their approval sets on a linear political spectrum. I imagine the society to be a representative…
Voter Compatibility In Interval Societies
In an interval society, voters are represented by intervals on the real line, corresponding to their approval sets on a linear political spectrum. I imagine the society to be a representative…
Approval Voting in Product Societies
TLDR
A general lower bound on agreement in a two-dimensional voting society is presented, and specific results for societies whose spectra are cylinders and tori are examined.
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.
Voting for Committees in Agreeable Societies
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Approval Ratios of Double-Interval Societies
If each convex set represents an interval of political positions on a spectrum that a voter approves of, then Helly’s theorem establishes a necessary and sufficient condition to guarantee that some…
Double-interval societies
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…
Approval Voting in Box Societies
Under approval voting, every voter may vote for any number of candidates. To model approval voting, we let a political spectrum be the set of all possible political positions, and let each voter have…
Approval Voting in Box Societies
Under approval voting, every voter may vote for any number of candidates. To model approval voting, we let a political spectrum be the set of all possible political positions, and let each voter have…
Approval Voting Theory with Multiple Levels of Approval
Approval voting is an election method in which voters may cast votes for as many candidates as they desire. This can be modeled mathematically by associating to each voter an approval region: a set…
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