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Axiomatization of Random Utility Model with Unobservable Alternatives

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  • Haruki Kono
  • Kota Saito
  • Alec Sandroni

Abstract

The random utility model is one of the most fundamental models in economics. Falmagne (1978) provides an axiomatization but his axioms can be applied only when choice frequencies of all alternatives from all subsets are observable. In reality, however, it is often the case that we do not observe choice frequencies of some alternatives. For such a dataset, we obtain a finite system of linear inequalities that is necessary and sufficient for the dataset to be rationalized by a random utility model. Moreover, the necessary and sufficient condition is tight in the sense that none of the inequalities is implied by the other inequalities, and dropping any one of the inequalities makes the condition not sufficient.

Suggested Citation

  • Haruki Kono & Kota Saito & Alec Sandroni, 2023. "Axiomatization of Random Utility Model with Unobservable Alternatives," Papers 2302.03913, arXiv.org, revised Aug 2023.
    • Handle: RePEc:arx:papers:2302.03913
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    References listed on IDEAS

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    1. Charalambos D. Aliprantis & Rosa L. Matzkin & Daniel L. McFadden & James C. Moore & Nicholas C. Yann (ed.), 2006. "Rationality and Equilibrium," Studies in Economic Theory, Springer, number 978-3-540-29578-5, March.
    2. Jean-Paul Doignon & Kota Saito, 2022. "Adjacencies on random ordering polytopes and flow polytopes," Papers 2207.06925, arXiv.org.
    3. Irène Charon & Olivier Hudry, 2010. "An updated survey on the linear ordering problem for weighted or unweighted tournaments," Annals of Operations Research, Springer, vol. 175(1), pages 107-158, March.
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    Cited by:

    1. Christopher Turansick, 2023. "An Alternative Approach for Nonparametric Analysis of Random Utility Models," Papers 2303.14249, arXiv.org, revised May 2024.

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