The problem of finding an aggregation procedure arises, as Arrow framed it, in connection with some given alternatives between which there is a choice is to be made. The nature of these alternatives depends on the kind of choice problem that is being studied. In the theory of elections, the alternatives are people who might stand as candidates in an election. In welfare economics they are different states of a society, such as distributions of income and labour requirements. The alternatives conventionally are referred to using lower case letters from the end of the alphabet as \(x, y, z, \ldots\); the set of all these alternatives is \(X\). The people whose tastes and values will inform the choice are assumed to be finite in number, and they are enumerated \(1, \ldots, n\).