Ordered choice probabilities in random utility models

André de Palma () and Karim Kilani
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Karim Kilani: LIRSA - Laboratoire interdisciplinaire de recherche en sciences de l'action - CNAM - Conservatoire National des Arts et Métiers [CNAM], IEMN - Institut d’Électronique, de Microélectronique et de Nanotechnologie - UMR 8520 - Centrale Lille - Institut supérieur de l'électronique et du numérique (ISEN) - UVHC - Université de Valenciennes et du Hainaut-Cambrésis - Université de Lille - CNRS - Centre National de la Recherche Scientifique - UPHF - Université Polytechnique Hauts-de-France

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Abstract: 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.

Keywords: Random utility models; Generalized Roy's identity; Logit; Ordered utilities; Order statistics; Probit (search for similar items in EconPapers)
Date: 2015-03-12
New Economics Papers: this item is included in nep-dcm and nep-upt
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