Voting Methods and Fairness Principles

Introduction and Outline

It’s just the greatest number of votes wins the election, right? Not so fast.

While a simple counting of votes can be an effective method in some situations, the theory of designing voting methods is a lot more complicated (and intriguing) than that. When one asks, “which voting method is the best,” this is both a mathematical and a philosophical question, not to mention a question that lends itself to interesting pedagogical opportunities in a math classroom. In this article I’m going to break this question into many pieces, but let’s start with defining the phrase “voting method.” A voting method is a procedure used on a preference table to determine a winning party out of two or more parties running in an election.

Now then, what’s a preference table? A preference table is a numerical table that indicates how many people voting in an election rank all of the candidates in a certain way. The table will have one column for each possible order of ranking the candidates. Since most examples used in a classroom setting have 3 candidates running in the election, I will indicate now that a preference table in this situation will have 6 columns. That’s because we can rank three candidates A, B, C in 6 ways:

A > B > C

A > C > B

C > A > B

C > B > A

B > A > C

B > C > A