The purpose of this paper is to report an experimental investigation of individual choice behavior in certain situations suggested by Debreu (1960) in his review of Luce’s book (1959). Let T denote the set of all possible alternatives from among which a subject might be required to choose. For any finite subset S of T (we call S the ‘offered set’) and any alternative x in S, let x(S) denote the probability that the subject, when choosing among the alternatives in S, will choose x. Thus x({x, y}) is the probability that the subject will choose from the pair {x, y} the alternative x rather than y. When x({x, y}) = 1, or equivalently j({x,y}) = 0,we say that x is absolutely preferred to y. The Luce model1 as presented in his book (1959) states that if no element of T is absolutely preferred to another element of T, then every element x of T is associated with a positive number v(x) (which we have called ‘strict utility of x’) such that, for every offered subset S of T,
$$x(S) = {{v(x)} \over {\sum\limits_{y \in S} {v(y)} }};$$
(that is, the elements of any offered set are chosen with probabilities proportional to their strict utilities).