Cumulative discrete choice

We present a discrete choice model in which a consumer's impression of each alternative is based on her memory of past experience with this choice, and is stochastically updated whenever the alternative is chosen. The consumer remembers a cumulative utility index per alternative, and, when an alternative is chosen, the index is updated by the addition of a random variable, interpreted as instantaneous utility. We prove that the frequencies of choice converge, with probability 1, to limit frequencies, which can be computed from the model's parameters.