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Cycle conditions for "Luce rationality"

Author

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  • Jose A. Rodrigues-Neto

    (Research School of Economics, Australian National University)

  • Matthew Ryan

    (Department of Economics and Finance, Auckland University of Technology)

  • James Taylor

    (Research School of Economics, Australian National University)

Abstract

We extend and refine conditions for "Luce rationality" (i.e., the existence of a Luce - or logit - model) in the context of stochastic choice. When choice probabilities satisfy positivity, we show that the cyclical independence (CI) condition of Ahumada and Ulku (2018) and Echenique and Saito (2019) is necessary and sufficient for Luce rationality, even if choice is only observed for a restricted set of menus. We then adapt results from the cycles approach (Rodrigues-Neto, 2009) to the common prior problem (Harsanyi, 1967-1968) to refine the CI condition, by reducing the number of cycle equations that need to be checked. A general algorithm is provided to identify a minimal sufficient set of equations (depending on the collection of menus for which choice is observed). Three cases are discussed in detail: (i) when choice is only observed from binary menus, (ii) when all menus contain a common default; and (iii) when all menus contain an element from a common binary default set. Investigation of case (i) leads to a refinement of the famous product rule.

Suggested Citation

  • Jose A. Rodrigues-Neto & Matthew Ryan & James Taylor, 2024. "Cycle conditions for "Luce rationality"," Working Papers 2024-03, Auckland University of Technology, Department of Economics.
    • Handle: RePEc:aut:wpaper:2024-03
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    References listed on IDEAS

    as
    1. Ahumada, Alonso & Ülkü, Levent, 2018. "Luce rule with limited consideration," Mathematical Social Sciences, Elsevier, vol. 93(C), pages 52-56.
    2. Chambers, Christopher P. & Turansick, Christopher, 2025. "The limits of identification in discrete choice," Games and Economic Behavior, Elsevier, vol. 150(C), pages 537-551.
    3. Matthew Kovach & Gerelt Tserenjigmid, 2022. "The Focal Luce Model," American Economic Journal: Microeconomics, American Economic Association, vol. 14(3), pages 378-413, August.
    4. Turansick, Christopher, 2022. "Identification in the random utility model," Journal of Economic Theory, Elsevier, vol. 203(C).
    5. Hellwig, Martin F., 2013. "From posteriors to priors via cycles: An addendum," Economics Letters, Elsevier, vol. 118(3), pages 455-458.
    6. Fiorini, Luciana C. & Rodrigues-Neto, José A., 2017. "Self-consistency, consistency and cycles in non-partitional knowledge models," Mathematical Social Sciences, Elsevier, vol. 87(C), pages 11-21.
    7. Hellman, Ziv & Samet, Dov, 2012. "How common are common priors?," Games and Economic Behavior, Elsevier, vol. 74(2), pages 517-525.
    8. Hausman, Jerry & McFadden, Daniel, 1984. "Specification Tests for the Multinomial Logit Model," Econometrica, Econometric Society, vol. 52(5), pages 1219-1240, September.
    9. José Rodrigues-Neto, 2014. "Monotonic models and cycles," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(2), pages 403-413, May.
    10. John C. Harsanyi, 1967. "Games with Incomplete Information Played by "Bayesian" Players, I-III Part I. The Basic Model," Management Science, INFORMS, vol. 14(3), pages 159-182, November.
    11. H.D. Block & Jacob Marschak, 1959. "Random Orderings and Stochastic Theories of Response," Cowles Foundation Discussion Papers 66, Cowles Foundation for Research in Economics, Yale University.
    12. Rodrigues-Neto, José Alvaro, 2012. "The cycles approach," Journal of Mathematical Economics, Elsevier, vol. 48(4), pages 207-211.
    13. Rodrigues-Neto, José Alvaro, 2009. "From posteriors to priors via cycles," Journal of Economic Theory, Elsevier, vol. 144(2), pages 876-883, March.
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