Ordered choice probabilities in random utility models
Résumé
We prove a general identity which states that any element of a tuple (ordered set) can be obtained as an alternating binomial weighted sum of rst elements of some sub-tuples. The identity is then applied within the random utility models framework where any alternative's ordered choice probability (the probability that it has a given rank) is expressed with respect to standard best choice probabilities. The logit and the logsum formulas are extended to their ordered choice counterparts. In a symmetric case, we compare for the probit and the logit, the surplus loss due to the withdrawal of a product with the damage due to the loss of a rank.
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