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

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Citation Type

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Voter Compatibility In Interval Societies
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TLDR
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References

SHOWING 1-10 OF 43 REFERENCES
Going from theory to practice: the mixed success of approval voting
TLDR
Ballot data from some of the societies that adopted AV are used to compare theoretical results with experience, including the nature of voting under AV and the kinds of candidates that are elected.
A Helly Type Conjecture
TLDR
There is no k such that Πk2 implies 2 -pierceability for all finite families of convex sets in the plane, so it is natural to propose the following conjecture.
Intersection Patterns of Convex Sets
In Chapter 1 we covered three simple but basic theorems in the theory of convexity: Helly’s, Radon’s, and Caratheodory’s. For each of them we present one closely related but more difficult theorem in…
Sperner and KKM-type theorems on trees and cycles
In this paper we prove a new combinatorial theorem for labellings of trees, and show that it is equivalent to a KKM-type theorem for finite covers of trees and to discrete and continuous fixed point…
Progress on perfect graphs
TLDR
The main aspects of perfect graphs and their relevance are surveyed and the recent proof of the Strong Perfect Graph Conjecture of Berge from 1961 is outlined.
The zero error capacity of a noisy channel
  • C. Shannon
  • Computer Science
    IRE Trans. Inf. Theory
  • 1956
TLDR
It is shown that while the ordinary capacity of a memoryless channel with feedback is equal to that of the same channel without feedback, the zero error capacity may be greater and a solution is given to the problem of evaluating C_oF.
Lectures on discrete geometry
  • J. Matousek
  • Mathematics
    Graduate texts in mathematics
  • 2002
TLDR
This book is primarily a textbook introduction to various areas of discrete geometry, in which several key results and methods are explained, in an accessible and concrete manner, in each area.
The Columbia dictionary of quotations
Entertaining and easy to use, The Columbia Dictionary of Quotations brings together more than 18,000 fresh and intriguing remarks, witticisms, judgments, and observations on 1,500 alphabetically…
ω-Perfect graphs
Abstractω-Perfect graph is defined and some classes of ω-perfect graphs are described, although the characterization of the complete class of ω-perfect graphs remains an open question. A bound on the…
A Special Planar Satisfiability Problem and a Consequence of Its NP-completeness
...
...