Voting, the Symmetric Group, and Representation Theory

Authors

Zajj Daugherty '05, Harvey Mudd CollegeFollow
Alexander K. Eustis '06, Harvey Mudd CollegeFollow
Gregory Minton '08, Harvey Mudd CollegeFollow
Michael E. Orrison, Harvey Mudd CollegeFollow

Student Co-author

HMC Undergraduate

Document Type

Article

Department

Mathematics (HMC)

Publication Date

12-17-2009

Abstract

We show how voting may be viewed naturally from an algebraic perspective by viewing voting profiles as elements of certain well-studied QS_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.

Comments

Publisher PDF posted with permission.

Rights Information

© 2009 Mathematical Association of America

Recommended Citation

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.