Abstract
It is trivial to tally a plurality election; just count how many voters have each candidate top-ranked. Surprisingly, when this elementary description is used to analyze the procedure, it quickly introduces mathematical complications that severely limit what can be learned.
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This 615 value is correct but misleading; it is the number of rankings preserving the identity of a voter. But, if only Carl and Martha interchange preferences, no change occurs in the election outcome. Thus anonymity, where the identities of the voters are irrelevant, reduces the number of rankings. When it only matters how many voters have each ranking, 15 voters generate 14,484 different profiles. But, where did this value come from? This computation, in itself, underscores the complexities associated with a discrete analysis. Moreover, when one considers what happens with 1, 2, …, 15, 16, … voters, millions upon millions of different voter arrangements emerge.
This means that if ci ≻ cj and cj≻ ck, then ci ≻ ck. So, with “transitivity” the binary rankings of certain pairs of candidates imposes a particular ranking on other pairs of candidates. These ideas are described in Sect. 3.1.
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© 1995 Springer-Verlag Berlin Heidelberg
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Saari, D.G. (1995). Geometry for Positional and Pairwise Voting. In: Basic Geometry of Voting. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-57748-2_2
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DOI: https://doi.org/10.1007/978-3-642-57748-2_2
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