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Ordered choice probabilities in random utility models

Author

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  • André de Palma

    (ENS Cachan - École normale supérieure - Cachan, X-DEP-ECO - Département d'Économie de l'École Polytechnique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris)

  • 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)

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.

Suggested Citation

  • André de Palma & Karim Kilani, 2015. "Ordered choice probabilities in random utility models," Working Papers hal-01130603, HAL.
    • Handle: RePEc:hal:wpaper:hal-01130603
    Note: View the original document on HAL open archive server: https://hal.science/hal-01130603
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    References listed on IDEAS

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    1. Steven Berry & James Levinsohn & Ariel Pakes, 2004. "Differentiated Products Demand Systems from a Combination of Micro and Macro Data: The New Car Market," Journal of Political Economy, University of Chicago Press, vol. 112(1), pages 68-105, February.
    2. Daniel McFadden, 2001. "Economic Choices," American Economic Review, American Economic Association, vol. 91(3), pages 351-378, June.
    3. Train,Kenneth E., 2009. "Discrete Choice Methods with Simulation," Cambridge Books, Cambridge University Press, number 9780521747387, November.
    4. Greene,William H. & Hensher,David A., 2010. "Modeling Ordered Choices," Cambridge Books, Cambridge University Press, number 9780521194204, January.
    5. André de Palma & Karim Kilani & Gilbert Laffond, 2013. "Best and worst choices," Working Papers halshs-00825656, HAL.
    6. Beggs, S. & Cardell, S. & Hausman, J., 1981. "Assessing the potential demand for electric cars," Journal of Econometrics, Elsevier, vol. 17(1), pages 1-19, September.
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    Cited by:

    1. Delle Site, Paolo & Kilani, Karim & Gatta, Valerio & Marcucci, Edoardo & de Palma, André, 2019. "Estimation of consistent Logit and Probit models using best, worst and best–worst choices," Transportation Research Part B: Methodological, Elsevier, vol. 128(C), pages 87-106.
    2. Paolo Delle Site & Karim Kilani & Valerio Gatta & Edoardo Marcucci & André de Palma, 2018. "Estimation of Logit and Probit models using best, worst and best-worst choices," Working Papers hal-01953581, HAL.

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    More about this item

    Keywords

    Random utility models; Generalized Roy's identity; Logit; Ordered utilities; Order statistics; Probit;
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