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An experimental investigation of violations of transitivity in choice under uncertainty

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  • Michael Birnbaum

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  • Ulrich Schmidt

Abstract

Several models of choice under uncertainty imply systematic violations of transitivity of preference. Our experiments explored whether people show patterns of intransitivity predicted by these models. To distinguish "true" violations from those produced by "error", a model was fit in which each choice can have a different error rate and each person can have a different pattern of true preferences that does not need to be transitive. Error rate for a choice is estimated from preference reversals between repeated presentations of the same choice. Our results showed that very few people repeated intransitive patterns. We can retain the hypothesis that transitivity best describes the data of the vast majority of participants.
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Suggested Citation

  • 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.
  • Handle: RePEc:kap:jrisku:v:37:y:2008:i:1:p:77-91
    DOI: 10.1007/s11166-008-9043-z
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    Citations

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    Cited by:

    1. 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.
    2. Michael H. Birnbaum, 2012. "A statistical test of independence in choice data with small samples," Judgment and Decision Making, Society for Judgment and Decision Making, vol. 7(1), pages 97-109, January.
    3. Aurélien Baillon & Han Bleichrodt & Alessandra Cillo, 2015. "A Tailor-Made Test of Intransitive Choice," Operations Research, INFORMS, vol. 63(1), pages 198-211, February.
    4. Amélie Vrijdags, 2010. "An experimental investigation of transitivity in set ranking," Theory and Decision, Springer, vol. 68(1), pages 213-232, February.
    5. 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.
    6. 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).
    7. Axel Sonntag, 2013. "Search Costs in Consumer Product Choice: Does Delaying the Provision of Information increase Choice Efficiency?," Working Paper series, University of East Anglia, Centre for Behavioural and Experimental Social Science (CBESS) 13-05, School of Economics, University of East Anglia, Norwich, UK..
    8. 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.
    9. Michael H. Birnbaum, 2013. "True-and-error models violate independence and yet they are testable," Judgment and Decision Making, Society for Judgment and Decision Making, vol. 8(6), pages 717-737, November.
    10. Han Bleichrodt & Alessandra Cillo & Enrico Diecidue, 2010. "A Quantitative Measurement of Regret Theory," Management Science, INFORMS, vol. 56(1), pages 161-175, January.
    11. Ulrich Schmidt & Michael Stolpe, 2011. "Transitivity in health utility measurement: An experimental analysis," Health Economics Review, Springer, vol. 1(1), pages 1-4, December.
    12. repec:kap:jrisku:v:54:y:2017:i:1:d:10.1007_s11166-017-9251-5 is not listed on IDEAS
    13. Jerome R. Busemeyer & Jörg Rieskamp, 2014. "Psychological research and theories on preferential choice," Chapters,in: Handbook of Choice Modelling, chapter 3, pages 49-72 Edward Elgar Publishing.
    14. Michael H. Birnbaum & Jeffrey P. Bahra, 2012. "Testing transitivity of preferences using linked designs," Judgment and Decision Making, Society for Judgment and Decision Making, vol. 7(5), pages 524-567, September.
    15. Sonntag, Axel, 2015. "Search costs and adaptive consumers: Short time delays do not affect choice quality," Journal of Economic Behavior & Organization, Elsevier, vol. 113(C), pages 64-79.
    16. Michael H. Birnbaum & Ulrich Schmidt & Miriam D. Schneider, 2017. "Testing independence conditions in the presence of errors and splitting effects," Journal of Risk and Uncertainty, Springer, vol. 54(1), pages 61-85, February.
    17. Schmidt, Ulrich & Birnbaum, Michael, 2014. "The Impact of Experience on Violations of Independence and Coalescing," Annual Conference 2014 (Hamburg): Evidence-based Economic Policy 100463, Verein für Socialpolitik / German Economic Association.
    18. Stoye, Jörg, 2015. "Choice theory when agents can randomize," Journal of Economic Theory, Elsevier, vol. 155(C), pages 131-151.
    19. Michael H. Birnbaum & Daniel Navarro-Martinez & Christoph Ungemach & Neil Stewart & Edika G. Quispe-Torreblanca, 2016. "Risky Decision making: Testing for violations of transitivity predicted by an editing mechanism," Judgment and Decision Making, Society for Judgment and Decision Making, vol. 11(1), pages 75-91, January.
    20. Jean Desrochers & J. Francois Outreville, 2013. "Uncertainty, Ambiguity and Risk Taking: an experimental investigation of consumer behavior and demand for insurance," ICER Working Papers 10-2013, ICER - International Centre for Economic Research.
    21. Amélie Vrijdags, 2013. "Min- and Max-induced rankings: an experimental study," Theory and Decision, Springer, vol. 75(2), pages 233-266, August.

    More about this item

    Keywords

    Choice; Decision making; Errors; Regret theory; Transitivity; C91; D81;

    JEL classification:

    • C91 - Mathematical and Quantitative Methods - - Design of Experiments - - - Laboratory, Individual Behavior
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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