Showing papers by "Jacob Marschak published in 2007"

Stochastic models of choice behavior

Abstract: The notion of “utility” is fundamental in most current theories of human decision. The problem of determining the utility function of a given decision maker, however, presents grave difficulties. It is not sufficient to determine the decision maker's rank-order preference of choices, because such a rank-order preference would determine his utility only on an ordinal scale, not the interval scale required in many decision problems. The problem is further complicated by the fact that even the preference choices of the chooser are often inconsistent with each other. T o circumvent the latter difficulty, stochastic definitions of utilities have been proposed in which probabilities (frequencies) of preference choices become the basic data. Here the implications of some of these models are derived which enable the experimenter to decide whether a given model is consistent with a set of data. Appropriate statistical sampling tests are worked out.

Probabilities of choices among very similar objects: an experiment to decide between two models.

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).