PRESENTATION OF THE PROBLEM

In democratic society, the prevalent method of decision-making is majority rule. This method attempts to aggregate many individual views and opinions into a single social decision.

Suppose there is a community of three voters who must make a decision by choosing one of three alternatives (say, disarmament, cold war, or open war). A society that behaves rationally will establish a preference order with regard to the three alternatives on the basis of voter preferences, choosing the alternative that is the first preference. If, for example, the society establishes a preference order in which the first preference is disarmament, the second preference is cold war, and the third preference is open war, the choice will be for disarmament.

Majority rule is the natural way to make a social decision on the basis of voter preferences.

Consider the following example, known as the “voting paradox.”

A certain amount of the municipal budget is unspent and the city council must decide how to invest it. It has three options: investment in education, investment in security, investment in health. (The sum is too small to divide feasibly among the three options.)