PRUDENCE AND EXTENSIONALITY IN THEORIES OF PREFERENCE AND VALUE

Luce's axiom governing probabilities of choice is formulated as a prin ciple governing metalinguistic probabilities. If X, Y, W are sets of o ptions, and delta(X), delta(Y), delta(W) are sentences asserting that choice is made from these sets, then the axiom is If pi[delta(X)] not equal 0 and pi[delta(X boolean AND Y)] not equal 0, then pi(delta(X))[ delta(Y boolean AND W)] = pi(delta(X boolean AND Y))[delta(W)]pi(delta (X))[delta(Y)] where pi is a probability on sentences. The axiom is th en entailed by extensionality of the probability pi in company with a simple condition on probabilities of truth-functions. Conditions are a lso given under which the probability pi is uniquely represented by a probability on the sets of options. What look to be logical constraint s on the metalanguage entail a normative or prudential constraint. Deb reu's well-known counterinstance to the axiom as a principle governing probability of choice is examined and a novel and consistent interpre tation of the axiom is proposed.