Introduction

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? 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.
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. 
What do we mean by fair?  Fundamental Terms and Ideas 
Back to topics listing for section V. THE MATHEMATICS OF VOTING