IDEAS home Printed from https://ideas.repec.org/p/aut/wpaper/2024-03.html
   My bibliography  Save this paper

Cycle conditions for "Luce rationality"

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://www.aut.ac.nz/__data/assets/pdf_file/0009/884178/working-paper-2024_03.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Rodrigues-Neto, José Alvaro, 2012. "The cycles approach," Journal of Mathematical Economics, Elsevier, vol. 48(4), pages 207-211.
    2. 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.
    3. Luciana C. Fiorini & José A. Rodrigues-Neto, 2014. "Self-Consistency and Common Prior in Non-Partitional Knowledge Models," ANU Working Papers in Economics and Econometrics 2014-621, Australian National University, College of Business and Economics, School of Economics.
    4. José A. Rodrigues‐Neto, 2015. "Monotonic Knowledge Models, Cycles, Linear Versions and Auctions with Differential, Finite Information," The Economic Record, The Economic Society of Australia, vol. 91(S1), pages 25-37, June.
    5. José Alvaro Rodrigues-Neto, 2012. "Cycles of length two in monotonic models," ANU Working Papers in Economics and Econometrics 2012-587, Australian National University, College of Business and Economics, School of Economics.
    6. Hellwig, Martin F., 2013. "From posteriors to priors via cycles: An addendum," Economics Letters, Elsevier, vol. 118(3), pages 455-458.
    7. José Rodrigues-Neto, 2014. "Monotonic models and cycles," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(2), pages 403-413, May.
    8. Paul H. Y. Cheung & Yusufcan Masatlioglu, 2025. "Frame-dependent Random Utility," Papers 2502.00209, arXiv.org.
    9. Guilhem Lecouteux, 2018. "Bayesian game theorists and non-Bayesian players," The European Journal of the History of Economic Thought, Taylor & Francis Journals, vol. 25(6), pages 1420-1454, November.
    10. Hellman, Ziv & Samet, Dov, 2012. "How common are common priors?," Games and Economic Behavior, Elsevier, vol. 74(2), pages 517-525.
    11. Hellwig, Martin, 2022. "Incomplete-information games in large populations with anonymity," Theoretical Economics, Econometric Society, vol. 17(1), January.
    12. Chambers, Christopher P. & Masatlioglu, Yusufcan & Turansick, Christopher, 2024. "Correlated choice," Theoretical Economics, Econometric Society, vol. 19(3), July.
      • Christopher P. Chambers & Yusufcan Masatlioglu & Christopher Turansick, 2021. "Correlated Choice," Papers 2103.05084, arXiv.org, revised Mar 2023.
    13. Ziv Hellman, 2014. "Countable spaces and common priors," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(1), pages 193-213, February.
    14. Martin Hellwig, 2011. "Incomplete-Information Models of Large Economies with Anonymity: Existence and Uniqueness of Common Priors," Discussion Paper Series of the Max Planck Institute for Research on Collective Goods 2011_08, Max Planck Institute for Research on Collective Goods.
    15. Rehbeck, John, 2024. "A menu dependent Luce model with a numeraire," Journal of Mathematical Economics, Elsevier, vol. 110(C).
    16. 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).
    17. Chambers, Christopher P. & Turansick, Christopher, 2025. "The limits of identification in discrete choice," Games and Economic Behavior, Elsevier, vol. 150(C), pages 537-551.
    18. Arjun Seshadri & Johan Ugander, 2020. "Fundamental Limits of Testing the Independence of Irrelevant Alternatives in Discrete Choice," Papers 2001.07042, arXiv.org.
    19. Christian W. Bach & Andrés Perea, 2023. "Structure‐preserving transformations of epistemic models," Economic Inquiry, Western Economic Association International, vol. 61(3), pages 693-719, July.
    20. Duffy, Sean & Smith, John, 2020. "An economist and a psychologist form a line: What can imperfect perception of length tell us about stochastic choice?," MPRA Paper 99417, University Library of Munich, Germany.

    More about this item

    Keywords

    :;

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:aut:wpaper:2024-03. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Gail Pacheco (email available below). General contact details of provider: https://edirc.repec.org/data/fbautnz.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.