social choice

The study of the aggregation of individual preferences into a group choice, or group ordering. It had false dawns in medieval Europe, and again from 1785 to 1803, and from 1873 to 1876. In 1299 Ramon Lull proposed that the winner in a multicandidate election should be chosen by comparing the candidates with one another, two at a time. In 1435 Nicholas Cusanus proposed what has come to be known as the Borda or rank-order count for electing a Holy Roman Emperor. In 1785 Condorcet first discovered that majority rule could ‘cycle’ so that there might be majorities for a over b, for b over c, and for c over a, all at the same time. When there is such a majority-rule cycle, the concept ‘will of the people’ is meaningless because every possibility loses by a popular majority to at least one other. Condorcet's ideas were extensively discussed in French academic circles until 1803, but then lost, to be independently rediscovered by C. L. Dodgson (Lewis Carroll) in the 1870s and rediscovered by Duncan Black in the 1950s. Social choice as now understood was founded jointly by Black and by Kenneth Arrow, whose general impossibility theorem of 1951 uses majority-rule cycles on its way to the startling proof that any choice procedure which satisfies some apparently minimal conditions of fairness and rationality is potentially dictatorial.

Since 1951, social choice theory has grown explosively. Most work has been so mathematically uncompromising that neither politicians nor political scientists have understood it, nor have social choice theorists bothered to explain themselves. But its chief results matter for both political theory and political practice. They include: that the weak Pareto rule (‘if everybody prefers a to b, society should choose a’) is inconsistent with libertarianism; that no fair and non-random voting procedure is proof against manipulation; and that, when opinion is multidimensional, there is probably a global majority-rule cycle embracing all outcomes, even those which lose unanimously to some others. Social choice is just starting to penetrate the practical discussion of proportional representation.