Probabilities of Choices Among Very Similar Objects: An Experiment to Decide Between Two Models (1963)

Abstract

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).

The work described in this paper was supported by the Western Management Science Institute, University of California at Los Angeles, under its grant from the Ford Foundation, a grant from the General Electric Company, and a contract with the Office of Naval Research, Task Nonr 233(75). The statistical computations were carried out at the Western Data Processing Center, University of California at Los Angeles.