Interesting Esoterica

Approval Voting in Product Societies

Article by Kristen Mazur and Mutiara Sondjaja and Matthew Wright and Carolyn Yarnall
  • Published in 2017
  • Added on
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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 that is acceptable to a majority of the voters. Hardin developed an analogous result when the issue can be represented on a circular spectrum. We examine scenarios in which voters must make two decisions simultaneously. For example, if voters must decide on the day of the week to hold a meeting and the length of the meeting, then the space of possible options forms a cylindrical spectrum. Previous results do not apply to these multi-dimensional voting societies because a voter's preference on one issue often impacts their preference on another. We present a general lower bound on agreement in a two-dimensional voting society, and then examine specific results for societies whose spectra are cylinders and tori.

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BibTeX entry

@article{ApprovalVotinginProductSocieties,
	title = {Approval Voting in Product Societies},
	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 that is acceptable to a majority of the voters.
Hardin developed an analogous result when the issue can be represented on a
circular spectrum. We examine scenarios in which voters must make two decisions
simultaneously. For example, if voters must decide on the day of the week to
hold a meeting and the length of the meeting, then the space of possible
options forms a cylindrical spectrum. Previous results do not apply to these
multi-dimensional voting societies because a voter's preference on one issue
often impacts their preference on another. We present a general lower bound on
agreement in a two-dimensional voting society, and then examine specific
results for societies whose spectra are cylinders and tori.},
	url = {http://arxiv.org/abs/1703.09870v1 http://arxiv.org/pdf/1703.09870v1},
	author = {Kristen Mazur and Mutiara Sondjaja and Matthew Wright and Carolyn Yarnall},
	comment = {},
	urldate = {2017-03-30},
	archivePrefix = {arXiv},
	eprint = {1703.09870},
	primaryClass = {math.CO},
	year = 2017,
	collections = {protocols-and-strategies}
}