Discrete Applied Math Seminar by Kathryn Nyman Vote Freely: A Look at Kemeny and Borda on Relations

Speaker:

Kathryn Nyman, professor of mathematics, Willamette University

Title:

Vote Freely: A Look at Kemeny and Borda on Relations

Abstract:

The Kemeny rule has a natural interpretation in terms of minimizing the distance between the winner(s) of an election and the ballot profile. While the Borda count is not defined in terms of distances, it, like Kemeny, is determined by information on pairs of candidates, and so can be reframed as a minimization rule over a different set of alternatives. In this talk, we compare Borda and Kemeny from a geometric perspective on distance interpretations.

These interpretations are more fully realized when we loosen the constraints on the space of voter inputs. By allowing voters to indicate preferences on general relations among underlying alternatives, we are able to embed many common profile spaces as subspaces of a higher dimensional, highly symmetric space. This symmetry leads to elegant and simple eigenspace decompositions of the space of profiles, shedding light on results that seem less natural in restricted situations, such as voting on full rankings or partially ordered sets. This allows us to not only compare Borda and Kemeny, but to use the eigenvalues in reverse as tuning parameters to create and analyze methods which accentuate various features of the ballot, regardless of the set of ballots we allow.

Discrete Applied Math Seminar

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