IDEAS home Printed from https://ideas.repec.org/a/kap/theord/v75y2013i2p233-266.html
   My bibliography  Save this article

Min- and Max-induced rankings: an experimental study

Author

Listed:
  • Amélie Vrijdags

Abstract

The current paper is the first to report an experimental study of “Min- and Max-induced rankings” (MMIR), i.e., a family of set rankings that require preferences over sets to be induced from comparison of the best and/or worst elements within those sets. These MMIR do not perform well in predicting preferences over simple sets of monetary outcomes. In this paper, we investigate the axiomatic underpinnings of these models by means of pairwise choice experiments. From this investigation, some important conclusions can be drawn: Axioms that prevent rankings to be based on total-goodness, as well as monotonicity conditions (ensuring that replacing a set element with a better one results in a better set) cannot be refuted. Axioms that rule out any utilization of the relative difference in the values of the outcomes and axioms that prevent rankings to be based on average-goodness are all systematically violated. The Uniform Expected Utility (UEU) criterion seems to meet the apparent shortcomings of the MMIR. Some frequently occurring preference patterns, however, suggest that a significant portion of the participants uses neither a Min- or Max-induced ranking, nor UEU, but some other unspecified decision rule, possibly characterized by the tendency to prefer a diversification of uncertainty. Copyright Springer Science+Business Media New York 2013

Suggested Citation

  • Amélie Vrijdags, 2013. "Min- and Max-induced rankings: an experimental study," Theory and Decision, Springer, vol. 75(2), pages 233-266, August.
    • Handle: RePEc:kap:theord:v:75:y:2013:i:2:p:233-266
    DOI: 10.1007/s11238-012-9339-y
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s11238-012-9339-y
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s11238-012-9339-y?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. Birnbaum, Michael H. & Gutierrez, Roman J., 2007. "Testing for intransitivity of preferences predicted by a lexicographic semi-order," Organizational Behavior and Human Decision Processes, Elsevier, vol. 104(1), pages 96-112, September.
    2. Cohen, Michele & Jaffray, Jean-Yves, 1980. "Rational Behavior under Complete Ignorance," Econometrica, Econometric Society, vol. 48(5), pages 1281-1299, July.
    3. Victor DeMiguel & Lorenzo Garlappi & Raman Uppal, 2009. "Optimal Versus Naive Diversification: How Inefficient is the 1-N Portfolio Strategy?," The Review of Financial Studies, Society for Financial Studies, vol. 22(5), pages 1915-1953, May.
    4. Gravel, Nicolas & Marchant, Thierry & Sen, Arunava, 2018. "Conditional expected utility criteria for decision making under ignorance or objective ambiguity," Journal of Mathematical Economics, Elsevier, vol. 78(C), pages 79-95.
    5. Harless, David W & Camerer, Colin F, 1994. "The Predictive Utility of Generalized Expected Utility Theories," Econometrica, Econometric Society, vol. 62(6), pages 1251-1289, November.
    6. Michael H. Birnbaum & Jeffrey P. Bahra, 2007. "Gain-Loss Separability and Coalescing in Risky Decision Making," Management Science, INFORMS, vol. 53(6), pages 1016-1028, June.
    7. Amélie Vrijdags, 2010. "An experimental investigation of transitivity in set ranking," Theory and Decision, Springer, vol. 68(1), pages 213-232, February.
    8. Michael Birnbaum & Ulrich Schmidt, 2010. "Testing transitivity in choice under risk," Theory and Decision, Springer, vol. 69(4), pages 599-614, October.
    9. Herbert A. Simon, 1955. "A Behavioral Model of Rational Choice," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 69(1), pages 99-118.
    10. Arlegi, Ricardo, 2007. "Sequentially consistent rules of choice under complete uncertainty," Journal of Economic Theory, Elsevier, vol. 135(1), pages 131-143, July.
    11. Nitzan, Shmuel I. & Pattanaik, Prasanta K., 1984. "Median-based extensions of an ordering over a set to the power set: An axiomatic characterization," Journal of Economic Theory, Elsevier, vol. 34(2), pages 252-261, December.
    12. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    13. repec:cup:judgdm:v:3:y:2008:i::p:304-316 is not listed on IDEAS
    14. John D. Hey & Chris Orme, 2018. "Investigating Generalizations Of Expected Utility Theory Using Experimental Data," World Scientific Book Chapters, in: Experiments in Economics Decision Making and Markets, chapter 3, pages 63-98, World Scientific Publishing Co. Pte. Ltd..
    15. Ritxar Arlegi, 2003. "A note on Bossert, Pattanaik and Xu's “Choice under complete uncertainty: axiomatic characterization of some decision rules”," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 22(1), pages 219-225, August.
    16. Daniel Ellsberg, 1961. "Risk, Ambiguity, and the Savage Axioms," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 75(4), pages 643-669.
    17. Kelsey, David, 1993. "Choice under Partial Uncertainty," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 34(2), pages 297-308, May.
    18. Michael Birnbaum & Ulrich Schmidt, 2008. "An experimental investigation of violations of transitivity in choice under uncertainty," Journal of Risk and Uncertainty, Springer, vol. 37(1), pages 77-91, August.
    19. Ritxar Arlegi, 2001. "Rational Evaluation of Actions Under Complete Uncertainty," Documentos de Trabajo - Lan Gaiak Departamento de Economía - Universidad Pública de Navarra 0114, Departamento de Economía - Universidad Pública de Navarra.
    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. Jorge Alcalde-Unzu & Ricardo Arlegi & Miguel Ballester, 2013. "Uncertainty with ordinal likelihood information," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(2), pages 397-425, July.
    2. Amélie Vrijdags, 2010. "An experimental investigation of transitivity in set ranking," Theory and Decision, Springer, vol. 68(1), pages 213-232, February.
    3. Birnbaum, Michael H. & Schmidt, Ulrich, 2010. "Allais paradoxes can be reversed by presenting choices in canonical split form," Kiel Working Papers 1615, Kiel Institute for the World Economy (IfW Kiel).
    4. Vieider, Ferdinand M. & Cingl, Lubomír & Martinsson, Peter & Stojic, Hrvoje, 2013. "Separating attitudes towards money from attitudes towards probabilities: Stake effects and ambiguity as a test for prospect theory," Discussion Papers, WZB Junior Research Group Risk and Development SP II 2013-401, WZB Berlin Social Science Center.
    5. Gijs van de Kuilen & Peter P. Wakker, 2011. "The Midweight Method to Measure Attitudes Toward Risk and Ambiguity," Management Science, INFORMS, vol. 57(3), pages 582-598, March.
    6. Levon Barseghyan & Francesca Molinari & Ted O'Donoghue & Joshua C. Teitelbaum, 2013. "The Nature of Risk Preferences: Evidence from Insurance Choices," American Economic Review, American Economic Association, vol. 103(6), pages 2499-2529, October.
    7. Aurélien Baillon & Han Bleichrodt & Alessandra Cillo, 2015. "A Tailor-Made Test of Intransitive Choice," Operations Research, INFORMS, vol. 63(1), pages 198-211, February.
    8. Pavlo Blavatskyy, 2018. "A second-generation disappointment aversion theory of decision making under risk," Theory and Decision, Springer, vol. 84(1), pages 29-60, January.
    9. repec:cup:judgdm:v:8:y:2013:i:1:p:55-73 is not listed on IDEAS
    10. John Hey & Andrea Morone & Ulrich Schmidt, 2009. "Noise and bias in eliciting preferences," Journal of Risk and Uncertainty, Springer, vol. 39(3), pages 213-235, December.
    11. Shaw, W. Douglass & Woodward, Richard T., 2008. "Why environmental and resource economists should care about non-expected utility models," Resource and Energy Economics, Elsevier, vol. 30(1), pages 66-89, January.
    12. Dimmock, Stephen G. & Kouwenberg, Roy & Mitchell, Olivia S. & Peijnenburg, Kim, 2016. "Ambiguity aversion and household portfolio choice puzzles: Empirical evidence," Journal of Financial Economics, Elsevier, vol. 119(3), pages 559-577.
    13. Yun-shil Cha & Michelle Choi & Ying Guo & Michel Regenwetter & Chris Zwilling, 2013. "Reply: Birnbaum's (2012) statistical tests of independence have unknown Type-I error rates and do not replicate within participant," Judgment and Decision Making, Society for Judgment and Decision Making, vol. 8(1), pages 55-73, January.
    14. Stoye, Jörg, 2015. "Choice theory when agents can randomize," Journal of Economic Theory, Elsevier, vol. 155(C), pages 131-151.
    15. Maillet, Bertrand & Tokpavi, Sessi & Vaucher, Benoit, 2015. "Global minimum variance portfolio optimisation under some model risk: A robust regression-based approach," European Journal of Operational Research, Elsevier, vol. 244(1), pages 289-299.
    16. Schmidt, Ulrich & Neugebauer, Tibor, 2003. "An Experimental Investigation of the Role of Errors for Explaining Violations of Expected Utility," Hannover Economic Papers (HEP) dp-279, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    17. Michael H. Birnbaum & Jeffrey P. Bahra, 2012. "Separating response variability from structural inconsistency to test models of risky decision making," Judgment and Decision Making, Society for Judgment and Decision Making, vol. 7(4), pages 402-426, July.
    18. Amit Kothiyal & Vitalie Spinu & Peter Wakker, 2014. "An experimental test of prospect theory for predicting choice under ambiguity," Journal of Risk and Uncertainty, Springer, vol. 48(1), pages 1-17, February.
    19. Daniela Di Cagno & Arianna Galliera & Werner Güth & Francesca Marzo & Noemi Pace, 2017. "(Sub) Optimality and (non) optimal satisficing in risky decision experiments," Theory and Decision, Springer, vol. 83(2), pages 195-243, August.
    20. Jakusch, Sven Thorsten & Meyer, Steffen & Hackethal, Andreas, 2019. "Taming models of prospect theory in the wild? Estimation of Vlcek and Hens (2011)," SAFE Working Paper Series 146, Leibniz Institute for Financial Research SAFE, revised 2019.
    21. Irenaeus Wolff & Dominik Bauer, 2018. "Elusive Beliefs: Why Uncertainty Leads to Stochastic Choice and Errors," TWI Research Paper Series 111, Thurgauer Wirtschaftsinstitut, Universität Konstanz.

    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:kap:theord:v:75:y:2013:i:2:p:233-266. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.