• Corpus ID: 248085361

Piercing Numbers in Circular Societies

@inproceedings{Mazur2020PiercingNI,
  title={Piercing Numbers in Circular Societies},
  author={Kristen Mazur and Mutiara Sondjaja and Matthew L. Wright and Carolyn Yarnall},
  year={2020}
}
. 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 piercing number have a natural interpretation. In this paper, we explore piercing numbers in the setting where voter preferences can be modeled by congruent arcs on a circle – i.e., in fixed-length circular societies. Given a number of voters and the length of the voter preference arcs, we give bounds on… 

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References

SHOWING 1-9 OF 9 REFERENCES
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.
Piercing numbers in approval voting
Voting in Agreeable Societies
TLDR
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.
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.
Approximation Algorithms for Rectangle Piercing Problems
TLDR
This dissertation designs approximation algorithms for unit-height rectangles for piercing problems and considers the problem with restrictions like bounding the depth of a point and the width of the rectangles.
Maintenance of a Piercing Set for Intervals with Applications
TLDR
A linear-size dynamic data structure is presented, which enables us to compute a new minimum piercing set following an insertion or deletion in time O(c( S) log |S|), where c (S) is the size of the new minimum Piercing set.
Agreement in Circular Societies