The shift of focus from games to elections represents a rather dramatic change in the objects of our study. We turn from probabilities, payoffs, and winning strategies to questions of the fairness, equity, and correctness of electoral outcomes. We have seen, however, that an election is not so different from a game at the most basic level. Recall in Definition 2.7, we defined an election as a game producing an outcome called the social choice. In this chapter, we study the mechanism for producing this outcome, the voting method.

We begin with a discussion to motivate the idea of voter preferences. The summary table of voter preferences is called a preference table. We introduce this important device along with a number of voting methods that will be studied throughout the text. We conclude with a discussion of social preferences and social welfare.

Preference Rankings

In practice, most elections do not require voters to rank all the candidates. Usually a “vote” consists of simply an indication of first choice. As we have mentioned, the use of voter preferences is assumed to facilitate our mathematical analysis of elections. That said, we observe that there are elections that do explicitly involve preference rankings of the candidates. We give two “controversial” examples, both occurring in the year 1990.

The world of sports provides a number of examples of elections in which voters submit preference rankings for the candidates. The Heisman Trophy in college football and the Most Valuable Player (MVP) awards and Hall of Fame elections for many professional sports are notable examples. Our example is from the National Basketball Association (NBA).