On the independence from irrelevant alternatives in probabilistic choice models
Abstract Probabilistic choice models often invoke a behavioral assumption referred to as the independence from irrelevant alternatives. The implications of this condition have not been fully developed in probabilistic choice contexts. It is well known that nonpathological preferences may not exhibit the independence from irrelevant alternatives, which is apparently an assumption of convenience; and the obvious question is then whether the assumption is very restrictive. This paper addresses this question. A common model of probabilistic choice is constructed. A measure of the likelihood that independence from irrelevant alternatives holds is seen to arise naturally in this model. Given this measure, it is demonstrated that the condition will almost always fail to hold.