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arXiv · 1703.09870

Approval Voting in Product Societies

Kristen Mazur·Mutiara Sondjaja·Matthew Wright·Carolyn Yarnall
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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.

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Kristen Mazur, Mutiara Sondjaja, Matthew Wright, Carolyn Yarnall. 2017-03-29. Approval Voting in Product Societies. https://doi.org/10.1080/00029890.2018.1390370

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