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Reduction of Compound Lotteries with Objective Probabilities: Theory and Evidence

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  • Glenn W. Harrison
  • Jimmy Martínez-Correa
  • J. Todd Swarthout

Abstract

The reduction of compound lotteries (ROCL) has assumed a central role in the evaluation of behavior towards risk and uncertainty. We present experimental evidence on its validity in the domain of objective probabilities. Our experiment explicitly recognizes the impact that the random lottery incentive mechanism payment procedure may have on preferences, and so we collect data using both "1-in-1" and "1-in-K" payment procedures, where K>1. We do not find violations of ROCL when subjects are presented with only one choice that is played for money. However, when individuals are presented with many choices and random lottery incentive mechanism is used to select one choice for payoff, we do find violations of ROCL. These results are supported by both non-parametric analysis of choice patterns, as well as structural estimation of latent preferences. We find evidence that the model that best describes behavior when subjects make only one choice is the Rank-Dependent Utility model. When subjects face many choices, their behavior is better characterized by our source-dependent version of the Rank-Dependent Utility model which can account for violations of ROCL. We conclude that payment protocols can create distortions in experimental tests of basic axioms of decision theory.

Suggested Citation

  • Glenn W. Harrison & Jimmy Martínez-Correa & J. Todd Swarthout, 2012. "Reduction of Compound Lotteries with Objective Probabilities: Theory and Evidence," Experimental Economics Center Working Paper Series 2012-04, Experimental Economics Center, Andrew Young School of Policy Studies, Georgia State University, revised Jul 2015.
  • Handle: RePEc:exc:wpaper:2012-04
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    References listed on IDEAS

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    1. Loomes, Graham & Sugden, Robert, 1998. "Testing Different Stochastic Specifications of Risky Choice," Economica, London School of Economics and Political Science, vol. 65(260), pages 581-598, November.
    2. repec:feb:framed:0074 is not listed on IDEAS
    3. David Dillenberger, 2010. "Preferences for One‐Shot Resolution of Uncertainty and Allais‐Type Behavior," Econometrica, Econometric Society, vol. 78(6), pages 1973-2004, November.
    4. Segal, Uzi, 1990. "Two-Stage Lotteries without the Reduction Axiom," Econometrica, Econometric Society, vol. 58(2), pages 349-377, March.
    5. 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.
    6. Hans P. Binswanger, 1980. "Attitudes Toward Risk: Experimental Measurement in Rural India," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 62(3), pages 395-407.
    7. Segal, Uzi, 1987. "The Ellsberg Paradox and Risk Aversion: An Anticipated Utility Approach," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 28(1), pages 175-202, February.
    8. 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.
    9. James Cox & Vjollca Sadiraj & Ulrich Schmidt, 2015. "Paradoxes and mechanisms for choice under risk," Experimental Economics, Springer;Economic Science Association, vol. 18(2), pages 215-250, June.
    10. Starmer, Chris & Sugden, Robert, 1991. "Does the Random-Lottery Incentive System Elicit True Preferences? An Experimental Investigation," American Economic Review, American Economic Association, vol. 81(4), pages 971-978, September.
    11. Conlisk, John, 1989. "Three Variants on the Allais Example," American Economic Review, American Economic Association, vol. 79(3), pages 392-407, June.
    12. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
    13. Glenn W Harrison & John A List & Charles Towe, 2007. "Naturally Occurring Preferences and Exogenous Laboratory Experiments: A Case Study of Risk Aversion," Econometrica, Econometric Society, vol. 75(2), pages 433-458, March.
    14. Charles A. Holt & Susan K. Laury, 2002. "Risk Aversion and Incentive Effects," American Economic Review, American Economic Association, vol. 92(5), pages 1644-1655, December.
    15. Harless, David W., 1992. "Predictions about indifference curves inside the unit triangle : A test of variants of expected utility theory," Journal of Economic Behavior & Organization, Elsevier, vol. 18(3), pages 391-414, August.
    16. 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.
    17. Daniel Ellsberg, 1961. "Risk, Ambiguity, and the Savage Axioms," The Quarterly Journal of Economics, Oxford University Press, vol. 75(4), pages 643-669.
    18. Beattie, Jane & Loomes, Graham, 1997. "The Impact of Incentives upon Risky Choice Experiments," Journal of Risk and Uncertainty, Springer, vol. 14(2), pages 155-168, March.
    19. Eeckhoudt, Louis & Gollier, Christian & Schlesinger, Harris, 1996. "Changes in Background Risk and Risk-Taking Behavior," Econometrica, Econometric Society, vol. 64(3), pages 683-689, May.
    20. 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.
    21. John Quiggin, 2003. "Background risk in generalized expected utility theory," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 22(3), pages 607-611, October.
    22. Yoram Halevy, 2007. "Ellsberg Revisited: An Experimental Study," Econometrica, Econometric Society, vol. 75(2), pages 503-536, March.
    23. 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.
    24. 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.
    25. Segal, Uzi, 1988. "Does the Preference Reversal Phenomenon Necessarily Contradict the Independence Axiom?," American Economic Review, American Economic Association, vol. 78(1), pages 233-236, March.
    26. Karni, Edi & Safra, Zvi, 1987. ""Preference Reversal' and the Observability of Preferences by Experimental Methods," Econometrica, Econometric Society, vol. 55(3), pages 675-685, May.
    27. Gollier, Christian & Pratt, John W, 1996. "Risk Vulnerability and the Tempering Effect of Background Risk," Econometrica, Econometric Society, vol. 64(5), pages 1109-1123, September.
    28. Holt, Charles A, 1986. "Preference Reversals and the Independence Axiom," American Economic Review, American Economic Association, vol. 76(3), pages 508-515, June.
    29. Glenn Harrison & J. Swarthout, 2014. "Experimental payment protocols and the Bipolar Behaviorist," Theory and Decision, Springer, vol. 77(3), pages 423-438, October.
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    Cited by:

    1. David Dillenberger & Uzi Segal, 2013. "Skewed Noise," Boston College Working Papers in Economics 843, Boston College Department of Economics, revised 26 Jul 2016.
    2. Harrison, Glenn W. & Martínez-Correa, Jimmy & Swarthout, J. Todd & Ulm, Eric R., 2017. "Scoring rules for subjective probability distributions," Journal of Economic Behavior & Organization, Elsevier, vol. 134(C), pages 430-448.
    3. Cary Deck & Harris Schlesinger, 2016. "On the Robustness of Higher Order Risk Preferences," Working Papers 16-26, Chapman University, Economic Science Institute.
    4. Drichoutis, Andreas & Nayga, Rodolfo, 2013. "A reconciliation of time preference elicitation methods," MPRA Paper 46916, University Library of Munich, Germany, revised 12 May 2013.
    5. Philip Grossman & Catherine Eckel, 2015. "Loving the long shot: Risk taking with skewed lotteries," Journal of Risk and Uncertainty, Springer, vol. 51(3), pages 195-217, December.
    6. Cary Deck & Harris Schlesinger, 2014. "Consistency of Higher Order Risk Preferences," Econometrica, Econometric Society, vol. 82, pages 1913-1943, September.
    7. Loic Berger & Valentina Bosetti, 2016. "Ellsberg re-revisited: An experiment disentangling model uncertainty and risk aversion," Working Papers 576, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    8. Amalia Di Girolamo & Glenn W. Harrison & Morten I. Lau & J. Todd Swarthout, 2013. "Characterizing Financial and Statistical Literacy," Experimental Economics Center Working Paper Series 2013-04, Experimental Economics Center, Andrew Young School of Policy Studies, Georgia State University.
    9. Heinrich, Timo & Shachat, Jason, 2018. "The development of risk aversion and prudence in Chinese children and adolescents," MPRA Paper 86456, University Library of Munich, Germany.
    10. Galizzi, Matteo M. & Machado, Sara R. & Miniaci, Raffaele, 2016. "Temporal stability, cross-validity, and external validity of risk preferences measures: experimental evidence from a UK representative sample," LSE Research Online Documents on Economics 67554, London School of Economics and Political Science, LSE Library.
    11. repec:eee:reecon:v:72:y:2018:i:1:p:49-64 is not listed on IDEAS
    12. Glenn W. Harrison & Jia Min Ng, 2016. "Evaluating The Expected Welfare Gain From Insurance," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 83(1), pages 91-120, January.
    13. Harrison, Glenn W. & Martínez-Correa, Jimmy & Swarthout, J. Todd, 2014. "Eliciting subjective probabilities with binary lotteries," Journal of Economic Behavior & Organization, Elsevier, vol. 101(C), pages 128-140.
    14. Kim Kaivanto & Eike Kroll, 2014. "Alternation bias and reduction in St. Petersburg gambles," Working Papers 65600286, Lancaster University Management School, Economics Department.
    15. Giuseppe Attanasi & Christian Gollier & Aldo Montesano & Noemi Pace, 2014. "Eliciting ambiguity aversion in unknown and in compound lotteries: a smooth ambiguity model experimental study," Theory and Decision, Springer, vol. 77(4), pages 485-530, December.

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