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 this paper, we show that the Block-Marschak polynomials can be defined as the probabilities that the decision maker has to delete each alternative from the choice set when the choice probability system is stochastically rationalizable.
|Date of creation:||00 Jun 2002|
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