From Project Syndicate:
Human beings have always lived in groups, and their individual lives have invariably depended on group decisions. But the challenges of group choice can be daunting, particularly given the divergent interests and concerns of the group’s members. So, how should collective decision-making be carried out?
A dictator who wants to control every aspect of people’s lives will seek to ignore the preferences of everyone else. But that level of power is hard to achieve. More important, dictatorship of any kind can readily be seen to be a terrible way to govern a society.
So, for both ethical and practical reasons, social scientists have long investigated how the concerns of a society’s members can be reflected in one way or another in its collective decisions, even if the society is not fully democratic. For example, in the fourth century BC, Aristotle in Greece and Kautilya in India explored various possibilities of social choice in their classic books, Politics and Economics, respectively (the Sanskrit title of Kautilya’s book, Arthashastra, translates literally as “the discipline of material wellbeing”).
The study of social choice as a formal discipline first came into its own in the late eighteenth century, when the subject was pioneered by French mathematicians, particularly J. C. Borda and Marquis de Condorcet. The intellectual climate of the time was greatly influenced by the European Enlightenment, with its interest in reasoned construction of a social order, and its commitment to the creation of a society responsive to people’s preferences.
But the theoretical investigations of Borda, Condorcet, and others often yielded rather pessimistic results. For example, the so-called “voting paradox” presented by Condorcet showed that majority rule can reach an impasse when every alternative is defeated in voting by some other alternative, so that no alternative is capable of standing up to the challenge of every other alternative.
Social choice theory in its modern and systematic form owes its rigorous foundation to the work of Kenneth J. Arrow in his 1950 Columbia University PhD dissertation. Arrow’s thesis contained his famous “impossibility theorem,” an analytical result of breathtaking elegance and reach.
Arrow’s theorem shows that even very mild conditions of reasonableness in arriving at social decisions on the basis of simple preference rankings of a society’s individuals could not be simultaneously satisfied by any procedure. When the book based on his dissertation, Social Choice and Individual Values, was published in 1951, it became an instant classic.
Economists, political theorists, moral and political philosophers, sociologists, and even the general public rapidly took notice of what seemed like – and indeed was – a devastating result. Two centuries after visions of social rationality flowered in Enlightenment thinking, the project suddenly seemed, at least superficially, to be inescapably doomed.
It is important to understand why and how Arrow’s impossibility result comes about. Scrutiny of the formal reasoning that establishes the theorem shows that relying only on the preference rankings of individuals makes it difficult to distinguish between very dissimilar social choice problems. The usability of available information is further reduced by the combined effects of innocuous-seeming principles that are popular in informal discussions.