The opportunity, gravity and thurstone models of individual choice

Abstract

This paper traces the development of methods for analyzing people's choice of action. It shows that two empirical formulations, the gravity and opportunity models, are approximate solutions to a more natural description of individual behavior, called the Thurstone model. In this model, each person always picks the course of action that he thinks is the best available. The analyst, however, cannot predict the choice because he does not know the individual's exact value for each alternative. Nevertheless, the analyst can describe these values with probability distributions, and by appropriate calculations can determine the chance of each alternative being chosen. The difference between the three models arises in the method of describing the analyst's uncertainty about a person's values. The Thurstone model uses an independent Normal distribution for each alternative. The gravity model simplifies the calculations by substituting an approximation for this distribution. The opportunity model is the special form of the gravity model that occurs when the values of the opportunities are dispersed at uniform intervals. The greater accuracy of the Thurstone model has been confirmed by a test with data on automobile parking choices. Nevertheless, the gravity model is useful for preliminary calculations because it is easier to calculate. Although the opportunity model usually is less accurate than either of the other two models, the difference is negligible in many common situations.