IDEAS home Printed from https://ideas.repec.org/a/gam/jgames/v12y2021i3p57-d589968.html
   My bibliography  Save this article

A Note on Numerical Representations of Nested System of Strict Partial Orders

Author

Listed:
  • Dan Qin

    (NUCB Business School, Nagoya University of Commerce and Business, Nagoya 4700193, Japan)

Abstract

This note provides two numerical representations of a nested system of strict partial orders. The first representation is based on utility and threshold functions. We generalize the threshold representation of menu-dependent preferences by allowing the threshold to depend not only on the menu but also on the pair of alternatives under comparison. The threshold function can be interpreted as the distance between alternatives. The second representation is based on the aggregation of multi-dimensional preference. This representation describes a decision-making procedure where multiple criteria are gradually aggregated into an overall assessment.

Suggested Citation

  • Dan Qin, 2021. "A Note on Numerical Representations of Nested System of Strict Partial Orders," Games, MDPI, vol. 12(3), pages 1-9, July.
    • Handle: RePEc:gam:jgames:v:12:y:2021:i:3:p:57-:d:589968
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2073-4336/12/3/57/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2073-4336/12/3/57/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Tyson, Christopher J., 2008. "Cognitive constraints, contraction consistency, and the satisficing criterion," Journal of Economic Theory, Elsevier, vol. 138(1), pages 51-70, January.
    2. Masatlioglu, Yusufcan & Ok, Efe A., 2005. "Rational choice with status quo bias," Journal of Economic Theory, Elsevier, vol. 121(1), pages 1-29, March.
    3. Herzberger, Hans G, 1973. "Ordinal Preference and Rational Choice," Econometrica, Econometric Society, vol. 41(2), pages 187-237, March.
    4. Fuad Aleskerov & Denis Bouyssou & Bernard Monjardet, 2007. "Utility Maximization, Choice and Preference," Springer Books, Springer, edition 0, number 978-3-540-34183-3, December.
    5. Tyson, Christopher J., 2008. "Cognitive constraints, contraction consistency, and the satisficing criterion," Journal of Economic Theory, Elsevier, vol. 138(1), pages 51-70, January.
    6. Carlos Hervés‐Beloso & Hugo del Valle‐Inclán Cruces, 2019. "Continuous Preference Orderings Representable By Utility Functions," Journal of Economic Surveys, Wiley Blackwell, vol. 33(1), pages 179-194, February.
    7. Yusufcan Masatlioglu & Efe A. Ok, 2014. "A Canonical Model of Choice with Initial Endowments," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 81(2), pages 851-883.
    8. Bosi, Gianni & Herden, Gerhard, 2012. "Continuous multi-utility representations of preorders," Journal of Mathematical Economics, Elsevier, vol. 48(4), pages 212-218.
    9. Ok, Efe A., 2002. "Utility Representation of an Incomplete Preference Relation," Journal of Economic Theory, Elsevier, vol. 104(2), pages 429-449, June.
    10. Anand, Paul, 1993. "The Philosophy of Intransitive Preference," Economic Journal, Royal Economic Society, vol. 103(417), pages 337-346, March.
    11. 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.
    12. ,, 2016. "Monotone threshold representations," Theoretical Economics, Econometric Society, vol. 11(3), September.
    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. Kops, Christopher, 2022. "Cluster-shortlisted choice," Journal of Mathematical Economics, Elsevier, vol. 102(C).
    2. Aguiar, Victor H. & Kimya, Mert, 2019. "Adaptive stochastic search," Journal of Mathematical Economics, Elsevier, vol. 81(C), pages 74-83.
    3. Manzini, Paola & Mariotti, Marco & Tyson, Christopher J., 2011. "Manipulation of Choice Behavior," IZA Discussion Papers 5891, Institute of Labor Economics (IZA).
    4. repec:hal:psewpa:halshs-01998001 is not listed on IDEAS
    5. Elias Bouacida, 2021. "Identifying Choice Correspondences," Working Papers halshs-01998001, HAL.
    6. Walter Bossert & Yves Sprumont, 2009. "Non‐Deteriorating Choice," Economica, London School of Economics and Political Science, vol. 76(302), pages 337-363, April.
    7. Cosimo Munari, 2020. "Multi-utility representations of incomplete preferences induced by set-valued risk measures," Papers 2009.04151, arXiv.org.
    8. Juan P. Aguilera & Levent Ülkü, 2017. "On the maximization of menu-dependent interval orders," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(2), pages 357-366, February.
    9. Manzini, Paola & Mariotti, Marco & Tyson, Christopher J., 2016. "Partial knowledge restrictions on the two-stage threshold model of choice," Journal of Mathematical Economics, Elsevier, vol. 64(C), pages 41-47.
    10. Shaofang Qi, 2016. "A characterization of the n-agent Pareto dominance relation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(3), pages 695-706, March.
    11. Manzini, Paola & Mariotti, Marco & Tyson, Christopher J., 2016. "Partial knowledge restrictions on the two-stage threshold model of choice," Journal of Mathematical Economics, Elsevier, vol. 64(C), pages 41-47.
    12. Gerasimou, Georgios & Papi, Mauro, 2018. "Duopolistic competition with choice-overloaded consumers," European Economic Review, Elsevier, vol. 101(C), pages 330-353.
    13. M. Ali Khan & Metin Uyanık, 2021. "Topological connectedness and behavioral assumptions on preferences: a two-way relationship," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(2), pages 411-460, March.
    14. Elias Bouacida, 2021. "Identifying Choice Correspondences," Working Papers 327800275, Lancaster University Management School, Economics Department.
    15. Tyson, Christopher J., 2008. "Cognitive constraints, contraction consistency, and the satisficing criterion," Journal of Economic Theory, Elsevier, vol. 138(1), pages 51-70, January.
    16. Chambers, Christopher P. & Hayashi, Takashi, 2012. "Choice and individual welfare," Journal of Economic Theory, Elsevier, vol. 147(5), pages 1818-1849.
    17. Kovach, Matthew & Ülkü, Levent, 2020. "Satisficing with a variable threshold," Journal of Mathematical Economics, Elsevier, vol. 87(C), pages 67-76.
    18. Pivato, Marcus, 2013. "Multiutility representations for incomplete difference preorders," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 196-220.
    19. Bleile, Jörg, 2016. "Limited Attention in Case-Based Belief Formation," Center for Mathematical Economics Working Papers 518, Center for Mathematical Economics, Bielefeld University.
    20. 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.
    21. , & , & , J., 2013. "Two-stage threshold representations," Theoretical Economics, Econometric Society, vol. 8(3), September.

    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:gam:jgames:v:12:y:2021:i:3:p:57-:d:589968. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.