INVARIANCE OF ACHIEVED UTILITY IN RANDOM UTILITY-MODELS

The property in some random utility models that the distribution of ac hieved utility is invariant across alternatives (the invariance proper ty) is noteworthy as it applies to the multinomial logit model as well as to its generalization: the generalized extreme-value (GEV) models. GEV models constitute the most versatile tool yet known for dealing w ith discrete choice situations with a structure of similarity-that is, statistical dependence-among alternatives. The invariance property is obviously violated in practice for heterogeneous populations. Therefo re it has been argued that invariance constitutes a major problem for GEV models. In contrast these authors argue that invariance is a usefu l theoretical concept precisely by bringing out heterogeneity. Further , multiple segment GEV models are a suitable tool for dealing with het erogeneity-both theoretically and pragmatically. The class of random u tility models possessing the invariance property was characterized by Robertson and Strauss; called the RS class here. However, their proof was not complete. An alternative representation of the RS class is sug gested based on the notion of additive homogeneity. This new represent ation enables the authors to prove the RS characterization theorem and to simplify and systematize the proofs of many other results on RS-an d specifically GEV-models. Also, in the new representation, the charac terization is naturally stated in terms of the choice probabilities, a nd of the probability distribution of maximum utility. Assuming that t he distribution of actual choices is observable, the choice probabilit ies are particularly empirically meaningful. This motivates a study of the conditions for a choice probability structure to be RS representa ble. For the binary choice case conditions that are both necessary and sufficient are given.