IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/41182.html
   My bibliography  Save this paper

Multiutility representations for incomplete difference preorders

Author

Listed:
  • Pivato, Marcus

Abstract

A ``difference preorder'' is a (possibly incomplete) preorder on a space of state changes (rather than the states themselves); it encodes information about preference intensity, in addition to ordinal preferences. We find necessary and sufficient conditions for a difference preorder to be representable by a family of cardinal utility functions which take values in linearly ordered abelian groups. This has applications to interpersonal comparisons, social welfare, and decisions under uncertainty.

Suggested Citation

  • Pivato, Marcus, 2012. "Multiutility representations for incomplete difference preorders," MPRA Paper 41182, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:41182
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/41182/1/MPRA_paper_41182.pdf
    File Function: original version
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    2. Luca Rigotti & Chris Shannon, 2005. "Uncertainty and Risk in Financial Markets," Econometrica, Econometric Society, vol. 73(1), pages 203-243, January.
    3. Tyson, Christopher J., 2008. "Cognitive constraints, contraction consistency, and the satisficing criterion," Journal of Economic Theory, Elsevier, vol. 138(1), pages 51-70, January.
    4. Patrick Suppes & Muriel Winet, 1955. "An Axiomatization of Utility Based on the Notion of Utility Differences," Management Science, INFORMS, vol. 1(3-4), pages 259-270, 04-07.
    5. Marcus Pivato, 2013. "Risky social choice with incomplete or noisy interpersonal comparisons of well-being," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(1), pages 123-139, January.
    6. Matthew Rabin, 1998. "Psychology and Economics," Journal of Economic Literature, American Economic Association, vol. 36(1), pages 11-46, March.
    7. Paolo Ghirardato & Fabio Maccheroni & Massimo Marinacci & Marciano Siniscalchi, 2003. "A Subjective Spin on Roulette Wheels," Econometrica, Econometric Society, vol. 71(6), pages 1897-1908, November.
    8. YIlmaz, Özgür, 2008. "Utility representation of lower separable preferences," Mathematical Social Sciences, Elsevier, vol. 56(3), pages 389-394, November.
    9. Vicki Knoblauch, 2006. "Continuously Representable Paretian Quasi-Orders," Theory and Decision, Springer, vol. 60(1), pages 1-16, February.
    10. Michael Mandler, 2006. "Cardinality versus Ordinality: A Suggested Compromise," American Economic Review, American Economic Association, vol. 96(4), pages 1114-1136, September.
    11. Mandler, Michael, 2005. "Incomplete preferences and rational intransitivity of choice," Games and Economic Behavior, Elsevier, vol. 50(2), pages 255-277, February.
    12. Marcus Pivato, 2014. "Additive representation of separable preferences over infinite products," Theory and Decision, Springer, vol. 77(1), pages 31-83, June.
    13. Ok, Efe A., 2002. "Utility Representation of an Incomplete Preference Relation," Journal of Economic Theory, Elsevier, vol. 104(2), pages 429-449, June.
    14. Efe A. Ok & Pietro Ortoleva & Gil Riella, 2012. "Incomplete Preferences Under Uncertainty: Indecisiveness in Beliefs versus Tastes," Econometrica, Econometric Society, vol. 80(4), pages 1791-1808, July.
    15. Baucells, Manel & Shapley, Lloyd S., 2008. "Multiperson utility," Games and Economic Behavior, Elsevier, vol. 62(2), pages 329-347, March.
    16. Sprumont, Yves, 2001. "Paretian Quasi-orders: The Regular Two-Agent Case," Journal of Economic Theory, Elsevier, vol. 101(2), pages 437-456, December.
    17. Kaminski, B., 2007. "On quasi-orderings and multi-objective functions," European Journal of Operational Research, Elsevier, vol. 177(3), pages 1591-1598, March.
    18. Galaabaatar, Tsogbadral & Karni, Edi, 2012. "Expected multi-utility representations," Mathematical Social Sciences, Elsevier, vol. 64(3), pages 242-246.
    19. Özgür Evren, 2008. "On the existence of expected multi-utility representations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 35(3), pages 575-592, June.
    20. Marcus Pivato, 2015. "Social choice with approximate interpersonal comparison of welfare gains," Theory and Decision, Springer, vol. 79(2), pages 181-216, September.
    21. Tsogbadral Galaabaatar & Edi Karni, 2013. "Subjective Expected Utility With Incomplete Preferences," Econometrica, Econometric Society, vol. 81(1), pages 255-284, January.
    22. Kaushik Basu, 1982. "Determinateness of the Utility Function: Revisiting a Controversy of the Thirties," Review of Economic Studies, Oxford University Press, vol. 49(2), pages 307-311.
    23. Veronika Köbberling, 2006. "Strength of preference and cardinal utility," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 27(2), pages 375-391, January.
    24. Evren, Özgür & Ok, Efe A., 2011. "On the multi-utility representation of preference relations," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 554-563.
    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. Bosi, Gianni & Herden, Gerhard, 2016. "On continuous multi-utility representations of semi-closed and closed preorders," Mathematical Social Sciences, Elsevier, vol. 79(C), pages 20-29.
    2. Marcus Pivato, 2015. "Social choice with approximate interpersonal comparison of welfare gains," Theory and Decision, Springer, vol. 79(2), pages 181-216, September.
    3. Bosi, Gianni & Herden, Gerhard, 2014. "Topological spaces for which every closed and semi-closed preorder respectively admits a continuous multi-utility representation," MPRA Paper 53404, University Library of Munich, Germany.

    More about this item

    Keywords

    Preference intensity; cardinal utility; linearly ordered abelian group; social welfare; uncertainty;

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D60 - Microeconomics - - Welfare Economics - - - General

    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:pra:mprapa:41182. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Joachim Winter) or (Rebekah McClure). General contact details of provider: http://edirc.repec.org/data/vfmunde.html .

    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 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.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.