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On Graphical Methods in Stochastic Choice

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  • Christopher Turansick

Abstract

In recent years there has been an influx of papers which use graph theoretic tools to study stochastic choice. Fiorini (2004) serves as a base for this literature by providing a graphical representation of choice probabilities and showing that every interior node of this graph must satisfy inflow equals outflow. We show that this inflow equals outflow property is almost characteristic of choice probabilities. In doing so, we characterize choice probabilities through graph theoretic tools. We offer two applications of this result to random utility. First, we offer a novel axiomatization of random utility on an incomplete domain. Second, we construct a new hypothesis test for random utility which offers computational improvements over the hypothesis test of Kitamura and Stoye (2018).

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  • Christopher Turansick, 2023. "On Graphical Methods in Stochastic Choice," Papers 2303.14249, arXiv.org, revised Sep 2023.
    • Handle: RePEc:arx:papers:2303.14249
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    References listed on IDEAS

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    1. Yuichi Kitamura & Jörg Stoye, 2018. "Nonparametric Analysis of Random Utility Models," Econometrica, Econometric Society, vol. 86(6), pages 1883-1909, November.
    2. Stoye, Jörg, 2019. "Revealed Stochastic Preference: A one-paragraph proof and generalization," Economics Letters, Elsevier, vol. 177(C), pages 66-68.
    3. Haruki Kono & Kota Saito & Alec Sandroni, 2023. "Axiomatization of Random Utility Model with Unobservable Alternatives," Papers 2302.03913, arXiv.org, revised Aug 2023.
    4. Yannai A. Gonczarowski & Scott Duke Kominers & Ran I. Shorrer, 2019. "To Infinity and Beyond: A General Framework for Scaling Economic Theories," Papers 1906.10333, arXiv.org, revised Apr 2023.
    5. Shasikanta Nandeibam, 2009. "On probabilistic rationalizability," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 32(3), pages 425-437, March.
    6. Daniel McFadden, 2005. "Revealed stochastic preference: a synthesis," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(2), pages 245-264, August.
    7. Amartya K. Sen, 1971. "Choice Functions and Revealed Preference," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 38(3), pages 307-317.
    8. Turansick, Christopher, 2022. "Identification in the random utility model," Journal of Economic Theory, Elsevier, vol. 203(C).
    9. Jean-Paul Doignon & Kota Saito, 2022. "Adjacencies on random ordering polytopes and flow polytopes," Papers 2207.06925, arXiv.org.
    10. Bart Smeulders & Laurens Cherchye & Bram De Rock, 2021. "Nonparametric Analysis of Random Utility Models: Computational Tools for Statistical Testing," Econometrica, Econometric Society, vol. 89(1), pages 437-455, January.
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