Publications [#350520] of Shira Viel

Papers Published

  1. Barcelo, H; Bernstein, M; Bockting-Conrad, S; McNicholas, E; Nyman, K; Viel, S, Algebraic voting theory & representations of Sm≀Sn, Advances in Applied Mathematics, vol. 120 (September, 2020)
    (last updated on 2021/06/21)

    Abstract:
    We consider the problem of selecting an n-member 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≀Sn-module homomorphisms. In particular, we decompose the spaces of voter preferences and election results into simple QSm≀Sn-submodules 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.