[go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/a/eee/matsoc/v65y2013i1p21-30.html
   My bibliography  Save this article

Quasiconcave preferences on the probability simplex: A nonparametric analysis

Author

Listed:
  • Heufer, Jan
Abstract
A nonparametric approach is presented to test whether decisions on a probability simplex could be induced by quasiconcave preferences. Necessary and sufficient conditions are presented which can easily be tested. If the answer is affirmative, the methods developed here allow us to reconstruct bounds on indifference curves. Furthermore we can construct quasiconcave utility functions in analogy to the utility function constructed in the proof of Afriat’s Theorem. The approach is of interest for ex ante fairness considerations when a dictator is asked to choose probabilities to win an indivisible prize. It is also of interest for decisions under risk and stochastic choice. It allows nonparametric interpersonal comparisons.

Suggested Citation

  • Heufer, Jan, 2013. "Quasiconcave preferences on the probability simplex: A nonparametric analysis," Mathematical Social Sciences, Elsevier, vol. 65(1), pages 21-30.
    • Handle: RePEc:eee:matsoc:v:65:y:2013:i:1:p:21-30
    DOI: 10.1016/j.mathsocsci.2012.06.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0165489612000601
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.mathsocsci.2012.06.003?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Crawford, Vincent P., 1990. "Equilibrium without independence," Journal of Economic Theory, Elsevier, vol. 50(1), pages 127-154, February.
    2. repec:ebl:ecbull:v:4:y:2003:i:31:p:1-7 is not listed on IDEAS
    3. Forges, Françoise & Minelli, Enrico, 2009. "Afriat's theorem for general budget sets," Journal of Economic Theory, Elsevier, vol. 144(1), pages 135-145, January.
    4. Chiappori, Pierre-Andre & Rochet, Jean-Charles, 1987. "Revealed Preferences and Differentiable Demand: Notes and Comments," Econometrica, Econometric Society, vol. 55(3), pages 687-691, May.
    5. Albers Wulf & Selten Reinhard & Pope Robin & Vogt Bodo, 2000. "Experimental Evidence for Attractions to Chance," German Economic Review, De Gruyter, vol. 1(2), pages 113-130, May.
    6. ,, 2010. "Rationalizable voting," Theoretical Economics, Econometric Society, vol. 5(1), January.
    7. Raymond Fisman & Shachar Kariv & Daniel Markovits, 2007. "Individual Preferences for Giving," American Economic Review, American Economic Association, vol. 97(5), pages 1858-1876, December.
    8. Matzkin, Rosa L. & Richter, Marcel K., 1991. "Testing strictly concave rationality," Journal of Economic Theory, Elsevier, vol. 53(2), pages 287-303, April.
    9. Edi Karni & Zvi Safra, 2002. "Individual Sense of Justice: A Utility Representation," Econometrica, Econometric Society, vol. 70(1), pages 263-284, January.
    10. Syngjoo Choi & Raymond Fisman & Douglas Gale & Shachar Kariv, 2007. "Consistency, Heterogeneity, and Granularity of Individual Behavior under Uncertainty," Economics Working Papers 0076, Institute for Advanced Study, School of Social Science.
    11. Sopher & Narramore, 2000. "Stochastic Choice and Consistency in Decision Making Under Risk: An Experimental Study," Theory and Decision, Springer, vol. 48(4), pages 323-349, June.
    12. Camerer, Colin F & Ho, Teck-Hua, 1994. "Violations of the Betweenness Axiom and Nonlinearity in Probability," Journal of Risk and Uncertainty, Springer, vol. 8(2), pages 167-196, March.
    13. Edi Karni & Zvi Safra, 2008. "Moral sentiments and social choice," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 30(3), pages 427-446, April.
    14. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    15. William Neilson, 2006. "Axiomatic reference-dependence in behavior toward others and toward risk," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 28(3), pages 681-692, August.
    16. Alexander W. Cappelen & James Konow & Erik ?. S?rensen & Bertil Tungodden, 2013. "Just Luck: An Experimental Study of Risk-Taking and Fairness," American Economic Review, American Economic Association, vol. 103(4), pages 1398-1413, June.
    17. Syngjoo Choi & Raymond Fisman & Douglas Gale & Shachar Kariv, 2007. "Consistency and Heterogeneity of Individual Behavior under Uncertainty," American Economic Review, American Economic Association, vol. 97(5), pages 1921-1938, December.
    18. Taradas Bandyopadhyay & Indraneel Dasgupta & Prasanta Pattanaik, 2004. "A general revealed preference theorem for stochastic demand behavior," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 23(3), pages 589-599, March.
    19. Shasikanta Nandeibam, 2009. "On probabilistic rationalizability," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 32(3), pages 425-437, March.
    20. Machina, Mark J, 1985. "Stochastic Choice Functions Generated from Deterministic Preferences over Lotteries," Economic Journal, Royal Economic Society, vol. 95(379), pages 575-594, September.
    21. Karni, Edi & Safra, Zvi, 2002. "Intensity of the Sense of Fairness: Measurement and Behavioral Characterization," Journal of Economic Theory, Elsevier, vol. 105(2), pages 318-337, August.
    22. Edi Karni & Tim Salmon & Barry Sopher, 2008. "Individual sense of fairness: an experimental study," Experimental Economics, Springer;Economic Science Association, vol. 11(2), pages 174-189, June.
    23. Varian, Hal R, 1982. "The Nonparametric Approach to Demand Analysis," Econometrica, Econometric Society, vol. 50(4), pages 945-973, July.
    24. Douglas M. Gale & Shachar Kariv & Syngjoo Choi & Raymond Fisman, 2007. "Revealing Preferences Graphically: An Old Method Gets a New Tool Kit," American Economic Review, American Economic Association, vol. 97(2), pages 153-158, May.
    25. Bandyopadhyay, Taradas & Bandyopadhyay, Bandyopadhyay & Pattanaik, Prasanta K., 2002. "Demand Aggregation and the Weak Axiom of Stochastic Revealed Preference," Journal of Economic Theory, Elsevier, vol. 107(2), pages 483-489, December.
    26. Knoblauch, Vicki, 1992. "A Tight Upper Bound on the Money Metric Utility Function," American Economic Review, American Economic Association, vol. 82(3), pages 660-663, June.
    27. Chris Starmer, 2000. "Developments in Non-expected Utility Theory: The Hunt for a Descriptive Theory of Choice under Risk," Journal of Economic Literature, American Economic Association, vol. 38(2), pages 332-382, June.
    28. Martin Sandbu, 2008. "Axiomatic foundations for fairness-motivated preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 31(4), pages 589-619, December.
    29. Hal R. Varian, 1983. "Non-parametric Tests of Consumer Behaviour," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 50(1), pages 99-110.
    30. Chew, S H & Epstein, Larry G & Segal, U, 1991. "Mixture Symmetry and Quadratic Utility," Econometrica, Econometric Society, vol. 59(1), pages 139-163, January.
    31. Machina, Mark J, 1982. ""Expected Utility" Analysis without the Independence Axiom," Econometrica, Econometric Society, vol. 50(2), pages 277-323, March.
    32. Jean Fernand Nguema, 2003. "Sense of impartiality," Economics Bulletin, AccessEcon, vol. 4(31), pages 1-7.
    33. Bandyopadhyay, Taradas & Dasgupta, Indraneel & Pattanaik, Prasanta K., 1999. "Stochastic Revealed Preference and the Theory of Demand," Journal of Economic Theory, Elsevier, vol. 84(1), pages 95-110, January.
    34. Jan Heufer, 2009. "Stochastic homothetically revealed preference for tight stochastic demand functions," Economics Bulletin, AccessEcon, vol. 29(3), pages 2472-2477.
    35. Jan Heufer, 2011. "Stochastic revealed preference and rationalizability," Theory and Decision, Springer, vol. 71(4), pages 575-592, October.
    36. James Andreoni & John Miller, 2002. "Giving According to GARP: An Experimental Test of the Consistency of Preferences for Altruism," Econometrica, Econometric Society, vol. 70(2), pages 737-753, 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. Heufer, Jan, 2014. "Nonparametric comparative revealed risk aversion," Journal of Economic Theory, Elsevier, vol. 153(C), pages 569-616.

    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. Heufer, Jan, 2014. "Nonparametric comparative revealed risk aversion," Journal of Economic Theory, Elsevier, vol. 153(C), pages 569-616.
    2. Daniel R. Burghart, 2020. "The two faces of independence: betweenness and homotheticity," Theory and Decision, Springer, vol. 88(4), pages 567-593, May.
    3. Paul Feldman & John Rehbeck, 2022. "Revealing a preference for mixtures: An experimental study of risk," Quantitative Economics, Econometric Society, vol. 13(2), pages 761-786, May.
    4. Bin Miao & Songfa Zhong, 2018. "Probabilistic social preference: how Machina’s Mom randomizes her choice," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 65(1), pages 1-24, January.
    5. Heufer, Jan & Hjertstrand, Per, 2019. "Homothetic preferences revealed," Journal of Economic Behavior & Organization, Elsevier, vol. 157(C), pages 602-614.
    6. Smeulders, Bart & Crama, Yves & Spieksma, Frits C.R., 2019. "Revealed preference theory: An algorithmic outlook," European Journal of Operational Research, Elsevier, vol. 272(3), pages 803-815.
    7. Cappelen, Alexander W. & Kariv, Shachar & Sørensen, Erik Ø. & Tungodden, Bertil, 2023. "The development gap in economic rationality of future elites," Games and Economic Behavior, Elsevier, vol. 142(C), pages 866-878.
    8. Jan Heufer, 2014. "A geometric approach to revealed preference via Hamiltonian cycles," Theory and Decision, Springer, vol. 76(3), pages 329-341, March.
    9. Uttara Balakrishnan & Johannes Haushofer & Pamela Jakiela, 2020. "How soon is now? Evidence of present bias from convex time budget experiments," Experimental Economics, Springer;Economic Science Association, vol. 23(2), pages 294-321, June.
    10. Hiroki Nishimura & Efe A. Ok & John K.-H. Quah, 2017. "A Comprehensive Approach to Revealed Preference Theory," American Economic Review, American Economic Association, vol. 107(4), pages 1239-1263, April.
    11. Kircher, Philipp & Sandroni, Alvaro & Ludwig, Sandra, 2009. "Fairness: A Critique to the Utilitarian Approach," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 288, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
    12. Jan Heufer, 2013. "Testing revealed preferences for homotheticity with two-good experiments," Experimental Economics, Springer;Economic Science Association, vol. 16(1), pages 114-124, March.
    13. Pawel Dziewulski, 2021. "A comprehensive revealed preference approach to approximate utility maximisation," Working Paper Series 0621, Department of Economics, University of Sussex Business School.
    14. Joshua Lanier & Bin Miao & John K.-H. Quah & Songfa Zhong, 2024. "Intertemporal Consumption with Risk: A Revealed Preference Analysis," The Review of Economics and Statistics, MIT Press, vol. 106(5), pages 1319-1333, September.
    15. Sam Cosaert & Thomas Demuynck, 2015. "Revealed preference theory for finite choice sets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 59(1), pages 169-200, May.
    16. Pawe{l} Dziewulski & Joshua Lanier & John K. -H. Quah, 2024. "Revealed preference and revealed preference cycles: a survey," Papers 2405.08459, arXiv.org.
    17. Allen, Roy & Dziewulski, Paweł & Rehbeck, John, 2022. "Making sense of monkey business: Re-examining tests of animal rationality," Journal of Economic Behavior & Organization, Elsevier, vol. 196(C), pages 220-228.
    18. Fisman, Raymond & Jakiela, Pamela & Kariv, Shachar, 2017. "Distributional preferences and political behavior," Journal of Public Economics, Elsevier, vol. 155(C), pages 1-10.
    19. Dziewulski, Paweł, 2020. "Just-noticeable difference as a behavioural foundation of the critical cost-efficiency index," Journal of Economic Theory, Elsevier, vol. 188(C).
    20. Pawel Dziewulski, 2018. "Just-noticeable difference as a behavioural foundation of the critical cost-efficiency," Economics Series Working Papers 848, University of Oxford, Department of Economics.

    More about this item

    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:eee:matsoc:v:65:y:2013:i:1:p:21-30. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/505565 .

    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.