Voting, the symmetric group, and representation theory

We show how voting may be viewed naturally from an algebraic perspective by viewing voting profiles as elements of certain well-studied $\mathbb{Q}{S}_n$-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.