Stochastic rationality and Möbius inverse

Discrete choice theory is very much dominated by the paradigm of the maximization of a random utility, thus implying that the probability of choosing an alternative in a given set is equal to the sum of the probabilities of all the rankings for which this alternative comes first. This property is called stochastic rationality. In turn, the choice probability system is said to be stochastically rationalizable if and only if the Block–Marschak polynomials are all nonnegative. In the present paper, we show that each particular Block–Marschak polynomial can be defined as the probability that the decision-maker faces the loss in flexibility generated by the fact that a particular alternative has been deleted from the choice set.