IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2302.03913.html
   My bibliography  Save this paper

Axiomatization of Random Utility Model with Unobservable Alternatives

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2302.03913
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

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

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Christopher Turansick, 2023. "On Graphical Methods in Stochastic Choice," Papers 2303.14249, arXiv.org, revised Sep 2023.

    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. Simone Cerreia-Vioglio & David Dillenberger & Pietro Ortoleva & Gil Riella, 2019. "Deliberately Stochastic," American Economic Review, American Economic Association, vol. 109(7), pages 2425-2445, July.
      • Simone Cerreia-Vioglio & David Dillenberger & Pietro Ortoleva & Gil Riella, 2012. "Deliberately Stochastic," PIER Working Paper Archive 17-013, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 25 May 2017.
    2. Thierry Denœux & Marie-Hélène Masson, 2012. "Evidential reasoning in large partially ordered sets," Annals of Operations Research, Springer, vol. 195(1), pages 135-161, May.
    3. Olivier Hudry, 2015. "Complexity results for extensions of median orders to different types of remoteness," Annals of Operations Research, Springer, vol. 225(1), pages 111-123, February.
    4. Wooders, Myrna, 2008. "Market games and clubs," MPRA Paper 33968, University Library of Munich, Germany, revised Dec 2010.
    5. Tiwisina, Johannes & Külpmann, Philipp, 2016. "Probabilistic Transitivity in Sports," Center for Mathematical Economics Working Papers 520, Center for Mathematical Economics, Bielefeld University.
    6. Christopher P. Chambers & Federico Echenique & Nicolas S. Lambert, 2021. "Recovering Preferences From Finite Data," Econometrica, Econometric Society, vol. 89(4), pages 1633-1664, July.
    7. Jean-Paul Doignon & Kota Saito, 2022. "Adjacencies on random ordering polytopes and flow polytopes," Papers 2207.06925, arXiv.org.
    8. Olivier Hudry & Bernard Monjardet, 2010. "Consensus theories: An oriented survey," Documents de travail du Centre d'Economie de la Sorbonne 10057, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    9. S. S. Dabadghao & B. Vaziri, 2022. "The predictive power of popular sports ranking methods in the NFL, NBA, and NHL," Operational Research, Springer, vol. 22(3), pages 2767-2783, July.
    10. Orestes Bueno & John Cotrina, 2021. "Existence of Projected Solutions for Generalized Nash Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 191(1), pages 344-362, October.
    11. Allouch, Nizar & Wooders, Myrna, 2008. "Price taking equilibrium in economies with multiple memberships in clubs and unbounded club sizes," Journal of Economic Theory, Elsevier, vol. 140(1), pages 246-278, May.
    12. Rajeev Kohli & Khaled Boughanmi & Vikram Kohli, 2019. "Randomized Algorithms for Lexicographic Inference," Operations Research, INFORMS, vol. 67(2), pages 357-375, March.
    13. Juan Aparicio & Mercedes Landete & Juan F. Monge, 2020. "A linear ordering problem of sets," Annals of Operations Research, Springer, vol. 288(1), pages 45-64, May.
    14. Labbé, Martine & Landete, Mercedes & Monge, Juan F., 2023. "Bilevel integer linear models for ranking items and sets," Operations Research Perspectives, Elsevier, vol. 10(C).
    15. Gregorio Curello & Ludvig Sinander, 2023. "Agenda-Manipulation in Ranking," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 90(4), pages 1865-1892.
    16. Hudry, Olivier, 2012. "On the computation of median linear orders, of median complete preorders and of median weak orders," Mathematical Social Sciences, Elsevier, vol. 64(1), pages 2-10.
    17. Christopher Turansick, 2023. "On Graphical Methods in Stochastic Choice," Papers 2303.14249, arXiv.org, revised Sep 2023.
    18. Gregorio Curello & Ludvig Sinander, 2020. "Agenda-manipulation in ranking," Papers 2001.11341, arXiv.org, revised Sep 2022.
    19. Marina Agranov & Pietro Ortoleva, 2017. "Stochastic Choice and Preferences for Randomization," Journal of Political Economy, University of Chicago Press, vol. 125(1), pages 40-68.

    More about this item

    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:arx:papers:2302.03913. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.