Probabilistic Multidimensional Models of Pairwise Choice Data
Geert De Soete University of Ghent, Belgium
J. Douglas Carroll Graduate School of Management Rutgers University
The inconsistency of human choice behavior led to the development of probabilistic choice models. This inconsistency is apparent in two ways. First, a subject tends to be inconsistent over replications. If a subject is repeatedly presented the same set of choice alternatives and asked to indicate which alternative he or she most prefers, he or she will not always respond in the same manner. Second, as is well known (e.g., Tversky, 1972b), a subject often experiences considerable subjective uncertainty when making such preference judgments.
When formulating choice models, this inconsistency can be taken into account in different ways. One approach consists of considering each preference judgment as an event in a probability space. Such a conception results in a probabilistic choice model that predicts the probability that a subject will select a specific object in an offered set (called a feasible set) as the most preferred alternative.
Although in principle nothing prevents us from constructing choice models that account for choices on feasible sets of more than two alternatives, most probabilistic choice models only deal with pairwise choices (i.e., choices on feasible sets consisting of only two choice objects). There are two reasons for this restriction. First, calculating choice probabilities predicted by a model for choices on feasible sets of more than two objects is usually fairly complicated because it involves the numerical evaluation of multiple integrals (see chap. 1).