The purpose of this article is to present a sample from the panoply of
formal theories on voting
and elections to Statistical Science readers who have had
limited exposure to such work.
These abstract ideas provide a framework for understanding the context of the empirical articles
that follow in this volume. The primary focus of this theoretical literature is on the use of
mathematical formalism to describe electoral systems and outcomes by modeling both voting rules
and human behavior. As with empirical models, these constructs are
never perfect descriptors of reality, but instead form the basis for
understanding fundamental characteristics of the studied system. Our
focus is on providing a general, but not overly simplified, review of
these theories with practical examples. We end the article with a
thought experiment that applies different vote aggregation schemes to
the 2000 presidential election count in Florida, and we find that
alternative methods provide different results.