Arrow's theorem

The most famous theorem in the logic of social choice or voting. 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: (i) it must work from any possible set of individual orderings of alternatives; (ii) it must satisfy the Pareto principle, that if each person prefers x to y then society must prefer x to y ; (iii) for any subset of the alternatives, only the individuals' preferences over the alternatives in the subset of alternatives are to count; and (iv) non-dictatorship: there must be no individual whose preferences alone dictate the preferences of the society. The voters' paradox is a simple example of the kind of problem that arises.