Math @ Duke

Publications [#350520] of Shira Viel
Papers Published
 Barcelo, H; Bernstein, M; BocktingConrad, S; McNicholas, E; Nyman, K; Viel, S, Algebraic voting theory & representations of Sm≀Sn,
Advances in Applied Mathematics, vol. 120
(September, 2020) [doi]
(last updated on 2021/12/03)
Abstract: We consider the problem of selecting an nmember committee made up of one of m candidates from each of n distinct departments. Using an algebraic approach, we analyze positional voting procedures, including the Borda count, as QSm≀Snmodule homomorphisms. In particular, we decompose the spaces of voter preferences and election results into simple QSm≀Snsubmodules and apply Schur's Lemma to determine the structure of the information lost in the voting process. We conclude with a voting paradox result, showing that for sufficiently different weighting vectors, applying the associated positional voting procedures to the same set of votes can yield vastly different election outcomes.


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