Efficiency and the logit model

This paper discusses model building for discrete choice problems in the simplest case – the logit model. General model building principles are formulated and used in evaluating ways of deriving logit choice probabilities. The principles include that models should represent human behavior, and that the basic assumptions should be testable and refutable against observations. Three ways of deriving the logit model are considered; the Luce model, the additive random utility maximizing approach, and the efficiency approach. The equivalence of the logit formula and the independence of irrelevant alternatives assumption (the Luce model) is well known. It is also well known that the assumption of additive random utility maximization with extreme value distribution for the unobservable stochastic components implies the logit formula. The opposite implication does not hold. The principal merit of additive random utility maximizing is its coherence with standard economic theory. Its principal weakness is that the basic assumptions cannot be tested, since the stochastic components cannot be observed. The efficiency assumption – samples with higher total observable utility are more probable – is equivalent to the logit formula. The advantage of the efficiency approach lies in its simple, testable basic behavioral assumptions. The independence of irrelevant alternatives assumption is equivalent to the efficiency assumption. The additive random utility maximization approach and the efficiency approach are not equivalent.