Sometimes (inappropriately) called Arrow’s paradox. The most famous theorem in the logic of social choice or voting, proved by Stanford economist and 1972 Nobel prizewinner Kenneth Arrow (1921–2017), in his Social Choice and Individual Value of 1951. The theorem (properly entitled the general possibility theorem) shows the impossibility of a social welfare function satisfying some very weak constraints. These in essence are:

1. (i) it must work from any possible set of individual orderings of alternatives;

2. (ii) it must satisfy the Pareto principle, that if each person prefers x to y then society must prefer x to y;

3. (iii) for any subset of the alternatives, only the individuals’ preferences over the alternatives in the subset of alternatives are to count; and

4. (iv) non-dictatorship: there must be no individual whose preferences alone dictate the preferences of the society, no matter what are the preferences of other individuals.

The voters’ paradox is a simple example of the kind of inconsistency that arises. Subsequent work has often enlarged the basis on which a function might be constructed, for instance by taking account not only of preferences themselves, but of strength or propriety of preference. See also Sen.