# Introduction to the Mathematics of Voting

Democracy is the worst form
of Government except [for] all
those other forms that have
been tried from time to time.

Winston Churchill
 Voting theory is the mathematical treatment of the process by which democratic societies or groups resolve the many and conflicting opinions of the members of the group into a single choice of the group. A vote is an expression of a voter's preference about the outcome of an election.Why do we need a mathematical theory about something so simple as voting? How difficult could it be to find a simple, fair, and consistent procedure for determining the outcome of an election? Actually, when an election involves only 2 candidates (or alternatives), then the situation is as simple as you might have imagined. For instance, suppose there is an election between Janice and Betty for senior class president. How should the election be set up so that the result fairly expresses the wishes of the senior class? Click here to see.   The situation is very different, however, when an election involves more than two candidates or alternatives and we wish to rank each of them in order of preference (preferential voting). Mathematical economist Kenneth Arrow proved (in 1952) that there is NO consistent method of making a fair choice among three or more candidates with preferential voting. This remarkable result assures us that there is no single preferential election procedure that can always fairly decide the outcome of an election that involves more than two candidates or alternatives.