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On path independent stochastic choice

Author

Listed:
  • Ahn, David S.

    (Department of Economics, University of California, Berkeley)

  • Echenique, Federico

    (Division of the Humanities and Social Sciences, California Institute of Technology)

  • Saito, Kota

    (Division of the Humanities and Social Sciences, California Institute of Technology)

Abstract

We investigate stochastic choice when only the average and not the entire distribution of choices is observable, focusing attention on the popular Luce model. Choice is path independent if it is recursive, in the sense that choosing from a menu can be broken up into choosing from smaller submenus. While an important property, path independence is known to be incompatible with continuous choice. The main result of our paper is that a natural modification of path independence, that we call partial path independence, is not only compatible with continuity but ends up characterizing the ubiquitous Luce (or Logit) rule.

Suggested Citation

  • Ahn, David S. & Echenique, Federico & Saito, Kota, 2018. "On path independent stochastic choice," Theoretical Economics, Econometric Society, vol. 13(1), January.
    • Handle: RePEc:the:publsh:2653
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    References listed on IDEAS

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    1. Antoine Billot & Itzhak Gilboa & Dov Samet & David Schmeidler, 2012. "Probabilities as Similarity-Weighted Frequencies," World Scientific Book Chapters, in: Case-Based Predictions An Axiomatic Approach to Prediction, Classification and Statistical Learning, chapter 7, pages 169-184, World Scientific Publishing Co. Pte. Ltd..
    2. Chambers, Christopher P. & Hayashi, Takashi, 2010. "Bayesian consistent belief selection," Journal of Economic Theory, Elsevier, vol. 145(1), pages 432-439, January.
    3. Plott, Charles R, 1973. "Path Independence, Rationality, and Social Choice," Econometrica, Econometric Society, vol. 41(6), pages 1075-1091, November.
    4. Faruk Gul & Paulo Natenzon & Wolfgang Pesendorfer, 2014. "Random Choice as Behavioral Optimization," Econometrica, Econometric Society, vol. 82, pages 1873-1912, September.
    5. Chambers, Christopher P., 2008. "Consistent representative democracy," Games and Economic Behavior, Elsevier, vol. 62(2), pages 348-363, March.
    6. Kalai, Ehud & Megiddo, Nimrod, 1980. "Path Independent Choices," Econometrica, Econometric Society, vol. 48(3), pages 781-784, April.
    7. Faruk Gul & Wolfgang Pesendorfer, 2006. "Random Expected Utility," Econometrica, Econometric Society, vol. 74(1), pages 121-146, January.
    8. Machina, Mark J & Parks, Robert P, 1981. "On Path Independent Randomized Choice: Comment," Econometrica, Econometric Society, vol. 49(5), pages 1345-1347, September.
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    Cited by:

    1. Yves Breitmoser, 2021. "An axiomatic foundation of conditional logit," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 72(1), pages 245-261, July.
    2. Faro, José Heleno, 2023. "The Luce model with replicas," Journal of Economic Theory, Elsevier, vol. 208(C).
    3. Doğan, Serhat & Yıldız, Kemal, 2021. "Odds supermodularity and the Luce rule," Games and Economic Behavior, Elsevier, vol. 126(C), pages 443-452.
    4. Javier A. Birchenall, 2024. "Random choice and market demand," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 57(1), pages 165-198, February.

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    More about this item

    Keywords

    Luce model; stochastic choice; logit model; path independence;
    All these keywords.

    JEL classification:

    • D01 - Microeconomics - - General - - - Microeconomic Behavior: Underlying Principles
    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory

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