Abstract
The application of the theory of partially ordered sets to voting systems is an important development in the mathematical theory of elections. Many of the results in this area are on the comparative properties between traditional elections with linearly ordered ballots and those with partially ordered ballots. In this paper we present a scoring procedure, called the partial Borda count, that extends the classic Borda count to allow for arbitrary partially ordered preference rankings. We characterize the partial Borda count in the context of weighting procedures and in the context of social choice functions.
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Acknowledgments
We benefitted greatly from conversations about this work with Bill Zwicker. We are also very grateful to the reviewers and editors, whose detailed comments and suggestions led to revisions and a new result (Theorem 2) that we feel significantly improved the paper.
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Cullinan, J., Hsiao, S.K. & Polett, D. A Borda count for partially ordered ballots. Soc Choice Welf 42, 913–926 (2014). https://doi.org/10.1007/s00355-013-0751-1
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DOI: https://doi.org/10.1007/s00355-013-0751-1