Two principles of rationality

The theory of rational choice and preference, as it has been developed in the past few decades by economists and decision theorists, rests on a pair of principles. The first, the weak ordering principle (WO), as it is usually formulated, takes rational choice to consist in the maximization of a weak preference ordering defined over the set of feasible alternatives. Adopting the usual terminology of speaking of x as weakly preferred to y when x is either (strictly) preferred to y or x and y are indifferent, a preference relation weakly orders a feasible set X just in case it is (1) connected – if x and y are any two alternatives in X, then either x is weakly preferred to y or y is weakly preferred to x (possibly both), and (2) fully transitive – for any three alternatives x, y, and z in X, if x is weakly preferred to y, and y is weakly preferred to z, then x is weakly preferred to z. Correspondingly, choice can be said to maximize such an ordering on X when the alternative x chosen satisfies the condition that there be no other alternative y in X such that y is (strictly) preferred to x. As it turns out, however, there is a quite distinct condition that is also presupposed – albeit usually only implicitly – in the weak ordering principle, namely, that the ordering is context free.