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The Luce model with replicas

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  • Faro, José Heleno

Abstract

We propose the notion of replicas in the context of discrete choices and introduce axioms that characterize the Luce model with replicas. This model does not fall prey to the well-known “red bus-blue bus” example originally proposed by Debreu (1960) and later made famous by McFadden. Our model satisfies regularity, strong stochastic transitivity, and is a random utility model. Due to its simplicity, this model is more parsimonious than others aimed at overcoming the “duplicates problem”.

Suggested Citation

  • Faro, José Heleno, 2023. "The Luce model with replicas," Journal of Economic Theory, Elsevier, vol. 208(C).
    • Handle: RePEc:eee:jetheo:v:208:y:2023:i:c:s0022053122001867
    DOI: 10.1016/j.jet.2022.105596
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    References listed on IDEAS

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    1. McFadden, Daniel L., 1984. "Econometric analysis of qualitative response models," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 24, pages 1395-1457, Elsevier.
    2. Paola Manzini & Marco Mariotti, 2014. "Stochastic Choice and Consideration Sets," Econometrica, Econometric Society, vol. 82(3), pages 1153-1176, May.
    3. Matthew Kovach & Gerelt Tserenjigmid, 2022. "Behavioral Foundations of Nested Stochastic Choice and Nested Logit," Journal of Political Economy, University of Chicago Press, vol. 130(9), pages 2411-2461.
    4. Train,Kenneth E., 2009. "Discrete Choice Methods with Simulation," Cambridge Books, Cambridge University Press, number 9780521766555, August.
    5. Ahn, David S. & Echenique, Federico & Saito, Kota, 2018. "On path independent stochastic choice," Theoretical Economics, Econometric Society, vol. 13(1), January.
    6. Horan, Sean, 2021. "Stochastic semi-orders," Journal of Economic Theory, Elsevier, vol. 192(C).
    7. Faruk Gul & Paulo Natenzon & Wolfgang Pesendorfer, 2014. "Random Choice as Behavioral Optimization," Econometrica, Econometric Society, vol. 82, pages 1873-1912, September.
    8. Cerreia-Vioglio, Simone & Lindberg, Per Olov & Maccheroni, Fabio & Marinacci, Massimo & Rustichini, Aldo, 2021. "A canon of probabilistic rationality," Journal of Economic Theory, Elsevier, vol. 196(C).
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    Cited by:

    1. Pavlo R. Blavatskyy, 2024. "Debreu’s choice model," Theory and Decision, Springer, vol. 96(2), pages 297-310, March.
    2. Alós-Ferrer, Carlos & Mihm, Maximilian, 2025. "A characterization of the Luce choice rule for an arbitrary collection of menus," Journal of Economic Theory, Elsevier, vol. 223(C).

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    Keywords

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    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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