Voting, the symmetric group, and representation theory

Details Voting, the symmetric group, and representation theory Voting, the symmetric group, and representation theory

2007-12-17

arxiv.org/abs/0712.2837v1

Mathematics

Representation Theory

19 pages

Scientific paper

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.

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