Nothing Special   »   [go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2303.04522.html
   My bibliography  Save this paper

A Note on Invariant Extensions of Preorders

Author

Listed:
  • Peter Caradonna
  • Christopher P. Chambers
Abstract
We consider the problem of extending an acyclic binary relation that is invariant under a given family of transformations into an invariant preference. We show that when a family of transformations is commutative, every acyclic invariant binary relation extends. We find that, in general, the set of extensions agree on the ranking of many pairs that (i) are unranked by the original relation, and (ii) cannot be ranked by invariance or transitivity considerations alone. We interpret these additional implications as the out-of-sample predictions generated by invariance, and study their structure.

Suggested Citation

  • Peter Caradonna & Christopher P. Chambers, 2023. "A Note on Invariant Extensions of Preorders," Papers 2303.04522, arXiv.org.
    • Handle: RePEc:arx:papers:2303.04522
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2303.04522
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Weymark, John A., 2000. "A generalization of Moulin's Pareto extension theorem," Mathematical Social Sciences, Elsevier, vol. 39(2), pages 235-240, March.
    2. Freer, Mikhail & Martinelli, César, 2021. "A utility representation theorem for general revealed preference," Mathematical Social Sciences, Elsevier, vol. 111(C), pages 68-76.
    3. Gorno, Leandro, 2017. "A strict expected multi-utility theorem," Journal of Mathematical Economics, Elsevier, vol. 71(C), pages 92-95.
    4. Efe A. Ok & Gil Riella, 2014. "Topological Closure of Translation Invariant Preorders," Mathematics of Operations Research, INFORMS, vol. 39(3), pages 737-745, August.
    5. Demuynck, Thomas, 2009. "A general extension result with applications to convexity, homotheticity and monotonicity," Mathematical Social Sciences, Elsevier, vol. 57(1), pages 96-109, January.
    6. Juan Dubra & Fabio Maccheroni & Efe A. Ok, 2004. "Expected Utility Without the Completeness Axiom," Yale School of Management Working Papers ysm404, Yale School of Management.
    7. Chambers,Christopher P. & Echenique,Federico, 2016. "Revealed Preference Theory," Cambridge Books, Cambridge University Press, number 9781107087804, September.
    8. Dubra, Juan & Maccheroni, Fabio & Ok, Efe A., 2004. "Expected utility theory without the completeness axiom," Journal of Economic Theory, Elsevier, vol. 115(1), pages 118-133, March.
    9. Kotaro Suzumura, 1976. "Rational Choice and Revealed Preference," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 43(1), pages 149-158.
    10. Duggan, John, 1999. "A General Extension Theorem for Binary Relations," Journal of Economic Theory, Elsevier, vol. 86(1), pages 1-16, May.
    11. Ok, Efe A., 2002. "Utility Representation of an Incomplete Preference Relation," Journal of Economic Theory, Elsevier, vol. 104(2), pages 429-449, June.
    12. José Alcantud, 2009. "Conditional ordering extensions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 39(3), pages 495-503, June.
    13. Yoram Halevy, 2015. "Time Consistency: Stationarity and Time Invariance," Econometrica, Econometric Society, vol. 83, pages 335-352, January.
    14. Donaldson, David & Weymark, John A., 1998. "A Quasiordering Is the Intersection of Orderings," Journal of Economic Theory, Elsevier, vol. 78(2), pages 382-387, February.
    15. Nishimura, Hiroki & Ok, Efe A., 2016. "Utility representation of an incomplete and nontransitive preference relation," Journal of Economic Theory, Elsevier, vol. 166(C), pages 164-185.
    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. Peter Caradonna & Christopher P. Chambers, 2024. "Revealed Invariant Preference," Papers 2408.04573, arXiv.org.
    2. Chambers, Christopher P. & Miller, Alan D., 2018. "Benchmarking," Theoretical Economics, Econometric Society, vol. 13(2), May.
    3. Pivato, Marcus, 2009. "Social choice with approximate interpersonal comparisons of well-being," MPRA Paper 17060, University Library of Munich, Germany.
    4. Cosimo Munari, 2020. "Multi-utility representations of incomplete preferences induced by set-valued risk measures," Papers 2009.04151, arXiv.org.
    5. Mikhail Freer & César Martinelli, 2023. "An algebraic approach to revealed preference," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 75(3), pages 717-742, April.
    6. Eric Danan, 2010. "Randomization vs. Selection: How to Choose in the Absence of Preference?," Management Science, INFORMS, vol. 56(3), pages 503-518, March.
    7. McCarthy, David & Mikkola, Kalle & Thomas, Teruji, 2021. "Expected utility theory on mixture spaces without the completeness axiom," Journal of Mathematical Economics, Elsevier, vol. 97(C).
    8. Gorno, Leandro & Rivello, Alessandro T., 2023. "A maximum theorem for incomplete preferences," Journal of Mathematical Economics, Elsevier, vol. 106(C).
    9. Quartieri, Federico, 2022. "A unified view of the existence of maximals," Journal of Mathematical Economics, Elsevier, vol. 99(C).
    10. Cosimo Munari, 2021. "Multi-utility representations of incomplete preferences induced by set-valued risk measures," Finance and Stochastics, Springer, vol. 25(1), pages 77-99, January.
    11. Athanasios Andrikopoulos, 2017. "Generalizations of Szpilrajn's Theorem in economic and game theories," Papers 1708.04711, arXiv.org.
    12. Weixuan Xia, 2023. "Optimal Consumption--Investment Problems under Time-Varying Incomplete Preferences," Papers 2312.00266, arXiv.org.
    13. Freer, Mikhail & Martinelli, César, 2021. "A utility representation theorem for general revealed preference," Mathematical Social Sciences, Elsevier, vol. 111(C), pages 68-76.
    14. McCarthy, David & Mikkola, Kalle & Thomas, Teruji, 2020. "Utilitarianism with and without expected utility," Journal of Mathematical Economics, Elsevier, vol. 87(C), pages 77-113.
    15. Eric Danan & Thibault Gajdos & Jean-Marc Tallon, 2015. "Harsanyi's Aggregation Theorem with Incomplete Preferences," American Economic Journal: Microeconomics, American Economic Association, vol. 7(1), pages 61-69, February.
    16. Kraus, Alan & Sagi, Jacob S., 2006. "Inter-temporal preference for flexibility and risky choice," Journal of Mathematical Economics, Elsevier, vol. 42(6), pages 698-709, September.
    17. McCarthy, David & Mikkola, Kalle & Thomas, Teruji, 2016. "Utilitarianism with and without expected utility," MPRA Paper 72578, University Library of Munich, Germany.
    18. Amparo M. Mármol & Luisa Monroy & M. Ángeles Caraballo & Asunción Zapata, 2017. "Equilibria with vector-valued utilities and preference information. The analysis of a mixed duopoly," Theory and Decision, Springer, vol. 83(3), pages 365-383, October.
    19. Bosi, Gianni & Herden, Gerhard, 2012. "Continuous multi-utility representations of preorders," Journal of Mathematical Economics, Elsevier, vol. 48(4), pages 212-218.
    20. Susumu Cato, 2013. "Quasi-decisiveness, quasi-ultrafilter, and social quasi-orderings," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(1), pages 169-202, June.

    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:2303.04522. 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.