Thresholds and Transitivity in Stochastic Consumer Choice: A Multinomial Logit Analysis

In previous work, thresholds have been introduced to describe situations where the consumer is indifferent between any two alternatives. Krishnan (Krishnan, K. S. 1977. Incorporating thresholds of indifference in probabilistic choice models. Management Sci.23 (July) 1224–1233.) formalised thresholds as minimum perceivable differences between the utilities of the alternatives compared and incorporated such thresholds into the binary logit model.

The present paper provides an extension and application of the theory to situations where the decision maker is confronted with more than two alternatives. In such situations thresholds can lead to systematic and predictable intransitivity of indifference, violating a basic postulate of utility theory. Explicit probabilities of transitive and intransitive choices are derived within the framework of the multinomial logit model and the stochastic consumer theory associated with this model.

The empirical applicability and managerial usefulness of the proposed theory is illustrated using a transportation example with three alternatives. The data employed reflect actual travellers' use of interurban transport modes in Greece. Parameters are estimated by a maximum-likelihood technique, based on a gradient search method. The results support the existence of thresholds. The application has important policy implications.