We show how voting may be viewed naturally from an algebraic perspective by viewing voting profiles as elements of certain well-studied QSn-modules. By using only a handful of simple combinatorial objects (e.g., tabloids) and some basic ideas from representation theory (e.g., Schur's Lemma), this allows us to recast and extend some well-known results in the field of voting theory.
© 2009 Mathematical Association of America
Daugherty, Zajj, Alexander K. Eustis, Gregory Minton, and Michael E. Orrison. "Voting, the Symmetric Group, and Representation Theory." American Mathematical Monthly 116.8 (2009): 667-87. Print.