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Alternation bias and reduction in St. Petersburg gambles

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  • Kim Kaivanto
  • Eike Kroll

Abstract

Reduction of compound lotteries is implicit both in the statement of the St. Petersburg Paradox and in its resolution by Expected Utility (EU).We report three real-money choice experiments between truncated compound-form St. Petersburg gambles and their reduced-form equivalents. The first tests for differences in elicited Certainty Equivalents. The second develops the distinction between ‘weak-form’ and ‘strong-form’ rejection of Reduction, as well as a novel experimental task that verifiably implements Vernon Smith’s dominance precept. The third experiment checks for robustness against range and increment manipulation. In all three experiments the null hypothesis of Reduction is rejected, with systematic deprecation of the compound form in favor of the reduced form. This is consistent with the predictions of alternation bias. Together these experiments offer evidence that the Reduction assumption may have limited descriptive validity in modelling St. Petersburg gambles, whether by EU or non-EU theories.

Suggested Citation

  • Kim Kaivanto & Eike Kroll, 2014. "Alternation bias and reduction in St. Petersburg gambles," Working Papers 65600286, Lancaster University Management School, Economics Department.
  • Handle: RePEc:lan:wpaper:65600286
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    1. Marc Rieger & Mei Wang, 2006. "Cumulative prospect theory and the St. Petersburg paradox," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 28(3), pages 665-679, August.
    2. Keller, L Robin, 1985. "Testing of the 'reduction of compound alternatives' principle," Omega, Elsevier, vol. 13(4), pages 349-358.
    3. Kaivanto, Kim & Kroll, Eike B., 2012. "Negative recency, randomization device choice, and reduction of compound lotteries," Economics Letters, Elsevier, vol. 115(2), pages 263-267.
    4. Harrison, Glenn W. & Martínez-Correa, Jimmy & Swarthout, J. Todd, 2015. "Reduction of compound lotteries with objective probabilities: Theory and evidence," Journal of Economic Behavior & Organization, Elsevier, vol. 119(C), pages 32-55.
    5. Pavlo Blavatskyy, 2009. "Preference reversals and probabilistic decisions," Journal of Risk and Uncertainty, Springer, vol. 39(3), pages 237-250, December.
    6. Nicholas Bardsley & Robin Cubitt & Graham Loomes & Peter Moffatt & Chris Starmer & Robert Sugden, 2009. "Experimental Economics: Rethinking the Rules," Economics Books, Princeton University Press, edition 1, number 9074, March.
    7. Smith, Vernon L, 1982. "Microeconomic Systems as an Experimental Science," American Economic Review, American Economic Association, vol. 72(5), pages 923-955, December.
    8. Rachel Croson & James Sundali, 2005. "The Gambler’s Fallacy and the Hot Hand: Empirical Data from Casinos," Journal of Risk and Uncertainty, Springer, vol. 30(3), pages 195-209, May.
    9. Mohammed Abdellaoui & Aurelien Baillon & Laetitia Placido & Peter P. Wakker, 2011. "The Rich Domain of Uncertainty: Source Functions and Their Experimental Implementation," American Economic Review, American Economic Association, vol. 101(2), pages 695-723, April.
    10. Tversky, Amos & Kahneman, Daniel, 1992. "Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 297-323, October.
    11. Kaivanto, Kim, 2008. "Alternation Bias and the Parameterization of Cumulative Prospect Theory," EconStor Open Access Articles, ZBW - Leibniz Information Centre for Economics, pages 91-107.
    12. Danan, Eric, 2008. "Revealed preference and indifferent selection," Mathematical Social Sciences, Elsevier, vol. 55(1), pages 24-37, January.
    13. Terrell, Dek, 1994. "A Test of the Gambler's Fallacy: Evidence from Pari-mutuel Games," Journal of Risk and Uncertainty, Springer, vol. 8(3), pages 309-317, May.
    14. Pavlo R. Blavatskyy, 2005. "Back to the St. Petersburg Paradox?," Management Science, INFORMS, vol. 51(4), pages 677-678, April.
    15. Blavatskyy, Pavlo R., 2006. "Violations of betweenness or random errors?," Economics Letters, Elsevier, vol. 91(1), pages 34-38, April.
    16. Matthew Rabin, 2002. "Inference by Believers in the Law of Small Numbers," The Quarterly Journal of Economics, Oxford University Press, vol. 117(3), pages 775-816.
    17. Mohammed Abdellaoui & Laetitia Placido & Aurélien Baillon & P.P. Wakker, 2011. "The Rich Domain of Uncertainty: Source Functions and Their Experimental Implementation," Post-Print hal-00609214, HAL.
    18. John R. Hauser, 1978. "Consumer Preference Axioms: Behavioral Postulates for Describing and Predicting Stochastic Choice," Management Science, INFORMS, vol. 24(13), pages 1331-1341, September.
    19. Gneezy, U., 1996. "Probability Judgements in Multi-Stage Problems : Experimental Evidence of Systematic Biases," Discussion Paper 1996-01, Tilburg University, Center for Economic Research.
    20. Urs Fischbacher, 2007. "z-Tree: Zurich toolbox for ready-made economic experiments," Experimental Economics, Springer;Economic Science Association, vol. 10(2), pages 171-178, June.
    21. Mandler, Michael, 2005. "Incomplete preferences and rational intransitivity of choice," Games and Economic Behavior, Elsevier, vol. 50(2), pages 255-277, February.
    22. Wakker,Peter P., 2010. "Prospect Theory," Cambridge Books, Cambridge University Press, number 9780521765015.
    23. James C. Cox & Vjollca Sadiraj & Bodo Vogt, 2009. "On the empirical relevance of st. petersburg lotteries," Economics Bulletin, AccessEcon, vol. 29(1), pages 214-220.
    24. Ben Greiner, 2004. "The Online Recruitment System ORSEE 2.0 - A Guide for the Organization of Experiments in Economics," Working Paper Series in Economics 10, University of Cologne, Department of Economics.
    25. Kahneman, Daniel & Tversky, Amos, 1979. "Prospect Theory: An Analysis of Decision under Risk," Econometrica, Econometric Society, vol. 47(2), pages 263-291, March.
    26. Robin Cubitt & Chris Starmer & Robert Sugden, 1998. "On the Validity of the Random Lottery Incentive System," Experimental Economics, Springer;Economic Science Association, vol. 1(2), pages 115-131, September.
    27. Ben Greiner, 2004. "The Online Recruitment System ORSEE - A Guide for the Organization of Experiments in Economics," Papers on Strategic Interaction 2003-10, Max Planck Institute of Economics, Strategic Interaction Group.
    28. Drazen Prelec, 1998. "The Probability Weighting Function," Econometrica, Econometric Society, vol. 66(3), pages 497-528, May.
    29. Terrell, Dek, 1998. "Biases in Assessments of Probabilities: New Evidence from Greyhound Races," Journal of Risk and Uncertainty, Springer, vol. 17(2), pages 151-166, November.
    30. Yoram Halevy, 2007. "Ellsberg Revisited: An Experimental Study," Econometrica, Econometric Society, vol. 75(2), pages 503-536, March.
    31. Vernon L. Smith, 1969. "Measuring Nonmonetary Utilities in Uncertain Choices: The Ellsberg Urn," The Quarterly Journal of Economics, Oxford University Press, vol. 83(2), pages 324-329.
    32. Wilcox, Nathaniel T, 1993. "Lottery Choice: Incentives, Complexity and Decision Time," Economic Journal, Royal Economic Society, vol. 103(421), pages 1397-1417, November.
    33. Grether, David M & Plott, Charles R, 1979. "Economic Theory of Choice and the Preference Reversal Phenomenon," American Economic Review, American Economic Association, vol. 69(4), pages 623-638, September.
    34. Ulrich Schmidt & John D. Hey, 2018. "Are Preference Reversals Errors? An Experimental Investigation," World Scientific Book Chapters, in: Experiments in Economics Decision Making and Markets, chapter 15, pages 353-364, World Scientific Publishing Co. Pte. Ltd..
    35. Tversky, Amos & Wakker, Peter, 1995. "Risk Attitudes and Decision Weights," Econometrica, Econometric Society, vol. 63(6), pages 1255-1280, November.
    36. Elena Asparouhova & Michael Hertzel & Michael Lemmon, 2009. "Inference from Streaks in Random Outcomes: Experimental Evidence on Beliefs in Regime Shifting and the Law of Small Numbers," Management Science, INFORMS, vol. 55(11), pages 1766-1782, November.
    37. Marie Pfiffelmann, 2011. "Solving the St. Petersburg Paradox in cumulative prospect theory: the right amount of probability weighting," Theory and Decision, Springer, vol. 71(3), pages 325-341, September.
    38. Harrison, Glenn W, 1994. "Expected Utility Theory and the Experimentalists," Empirical Economics, Springer, vol. 19(2), pages 223-253.
    39. Doron Sonsino & Uri Benzion & Galit Mador, 2002. "The Complexity Effects on Choice with Uncertainty — Experimental Evidence," Economic Journal, Royal Economic Society, vol. 112(482), pages 936-965, October.
    40. Doron Sonsino, 2011. "A note on negativity bias and framing response asymmetry," Theory and Decision, Springer, vol. 71(2), pages 235-250, August.
    41. David J. Butler & Graham C. Loomes, 2007. "Imprecision as an Account of the Preference Reversal Phenomenon," American Economic Review, American Economic Association, vol. 97(1), pages 277-297, March.
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    Cited by:

    1. Matteo M. Marini, 2018. "20 years of emotions and risky choices in the lab: A meta-analysis," Working Papers 2018/14, Economics Department, Universitat Jaume I, Castellón (Spain).
    2. Paolo Crosetto & Antonio Filippin, 2016. "A theoretical and experimental appraisal of four risk elicitation methods," Experimental Economics, Springer;Economic Science Association, vol. 19(3), pages 613-641, September.

    More about this item

    Keywords

    St. Petersburg Paradox; reduction axiom; alternation bias; dominance precept; law of small numbers; test of indifference;

    JEL classification:

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

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