Abstract
We provide a novel but intuitive explanation for expected utility violations found in the Allais paradox: individuals are commonly averse to receiving nothing. We call this phenomenon the zero effect. Our laboratory experiments show support for the zero effect. By contrast, the evidence for the certainty effect is weak to nonexistent.
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Notes
For example, a similar experiment in Kahneman and Tversky (1979) finds that 12 out of 72 participants chose A over B, but 59 out of 72 chose \(A'\) over \(B'\). These numbers imply that at most 35% chose either both A and \(A'\) or both B and \(B'\), with the remainder violating expected utility theory.
For approaches staying within a triangle design that provide indirect tests by considering multiple triangles, see Appendix B.
Although allowing for indifference adds a complication, we permit it to rule out indifference as a cause of Allais-type behavior. See Harrison (1994).
If we include indifferences, there are five additional patterns of interest: IIIIII (expected utility); RRIRRR and IISIII (certainty effect), and ISSSSS and RIIIII (zero effect). We run our tests both including observations with indifferences and excluding observations with indifferences.
Littenberg et al. (2003) establish the reliability of pencil-and-paper instruments for tasks involving decisions under risk.
Our null hypotheses are that each predicted pattern occurs no more than due to chance, i.e., with probability \(1/64\). We also tested the non-EU patterns to see if they occur no more than due to chance conditional on non-EU choice, i.e., with probability \(1/62\). The results were the same.
To elaborate, we note that there are additional patterns consistent with the CCE, aside from the certainty effect and zero effect patterns. Recall from Definition 1 that the CCE depends only on decisions under two common consequences, \(c\in \{0,m\}\). Therefore, any pattern with riskier choice when c=0 than when c=m would be consistent with the CCE (e.g. \(R\_S\_\_\_\)).
We also consider numerous alternative tests, allowing for heterogeneity in trembles across common consequences, in the spirit of the true-and-error model of Birnbaum and Schmidt (2008), and tests that can be considered a simple version of the true-and-error model as in Loomes et al. (1991). In addition, we modified our main tests to include other forms of heterogeneity in trembles, such as errors that depend on presentation order or presentation style. We also allowed for individual heterogeneity in errors based on preferences, e.g., allowing for an EU type who prefers a safe lottery to have different rates of trembles than an EU type who prefers a risky lottery. None of these variations changed our main conclusions (details available from the authors on request).
We use the bootstrap method to estimate the standard error of the estimated parameters. For the bootstrap estimation, we re-sampled the experimental data 10,000 times.
References
Allais, M. (1953). Le comportement de l’homme rationnel devanti le risque, critique des postulates et axiomes de l’école Americaine. Econometrica, 21(4), 503–546.
Azrieli, Y., Chambers, C. P., & Healy, P. J. (2020). Incentives in experiments with objective lotteries. Experimental Economics, 23(1), 1–29.
Battalio, R. C., Kagel, J. H., & Jiranyakul, K. (1990). Testing between alternative models of choice under uncertainty: some initial results. Journal of Risk and Uncertainty, 3(1), 25–50.
Beattie, J., & Loomes, G. (1997). The impact of incentives upon risky choice experiments. Journal of Risk and Uncertainty, 14(2), 155–168.
Bhatia, S., & Loomes, G. (2017). Noisy preferences in risky choice: a cautionary note. Psychological Review, 124(5), 678–687.
Birnbaum, M. H., & Schmidt, U. (2008). An experimental investigation of violations of transitivity in choice under uncertainty. Journal of Risk and Uncertainty, 37(1), 77–91.
Blavatskyy, P., Ortmann, A., & Panchenko, V. (2020). On the experimental robustness of the Allais paradox. American Economic Journal: Microeconomics. Forthcoming.
Blavatskyy, P. R., & Pogrebna, G. (2010). Models of stochastic choice and decision theories: Why both are important for analyzing decisions. Journal of Applied Econometrics, 25(6), 963–986.
Camerer, C. F. (1989). An experimental test of several generalized utility theories. Journal of Risk and Uncertainty, 2(1), 61–104.
Camerer, C. F., & Ho, T. H. (1994). Violations of the betweenness axiom and nonlinearity in probability. Journal of Risk and Uncertainty, 8(2), 167–196.
Camerer, C. F., & Hogarth, R. M. (1999). The effects of financial incentives in experiments: a review and capital-labor framework. Journal of Risk and Uncertainty, 19(1–3), 7–42.
Conlisk, J. (1989). Three variants on the Allais example. American Economic Review, 79(3), 392–407.
Crosetto, P., & Filippin, A. (2016). A theoretical and experimental appraisal of four risk elicitation methods. Experimental Economics, 19(3), 613–641.
Cubitt, R., Starmer, C., & Sugden, R. (1998). Dynamic choice and the common ratio effect: an experimental investigation. The Economic Journal, 108(450), 1362–1380.
Fan, C. P. (2002). Allais paradox in the small. Journal of Economic Behavior and Organization, 49(3), 411–421.
Gottlieb, D. A., Weiss, T., & Chapman, G. B. (2007). The format in which uncertainty information is presented affects decision biases. Psychological Science, 18(3), 240–246.
Harless, D. W., & Camerer, C. F. (1994). The predictive utility of generalized expected utility theories. Econometrica, 62(6), 1251–1289.
Harman, J. L., & Gonzalez, C. (2015). Allais from experience: choice consistency, rare events, and common consequences in repeated decisions. Behavioral Decision Making, 28(4), 369–381.
Harrison, G. W. (1994). Expected utility theory and the experimentalists. Empirical Economics, 19(2), 223–253.
Harrison, G. W. (2006). Hypothetical bias over uncertain outcomes. In Using experimental (Ed.), List JA (pp. 41–69). Methods in Environmental and Resource Economics: Edward Elgar.
Kahneman, D., & Tversky, A. (1979). Prospect theory: an analysis of decision under risk. Econometrica, 47(2), 263–292.
Keller, L. R. (1985). The effects of problem representation on the sure-thing and substitution principles. Management Science, 31(6), 738–751.
Lévy-Garboua, L., Maafi, H., Masclet, D., & Terracol, A. (2012). Risk aversion and framing effects. Experimental Economics, 15(1), 128–144.
Littenberg, B., Partilo, S., Licata, A., & Kattan, M. W. (2003). Paper standard gamble: the reliability of a paper questionnaire to assess utility. Medical Decision Making, 23(6), 480–488.
Loomes, G., & Pogrebna, G. (2014). Measuring indvidual risk attitudes when preferences are imprecise. Economic Journal, 124(576), 569–593.
Loomes, G., Starmer, C., & Sugden, R. (1991). Observing violations of transitivity by experimental methods. Econometrica, 59(2), 425–439.
MacDonald, D.N., Wall, J.L. (1989). An experimental study of the allais paradox over losses: some preliminary evidence. Quarterly Journal of Business and Economics pp 43–60.
Machina, M. J. (1982). “Expected utility” analysis without the independence axiom. Econometrica, 50(2), 277–324.
Marschak, J. (1950). Rational behavior, uncertain prospects, and measurable utility. Econometrica, 18(2), 111–141.
Moskowitz, H. (1974). Effects of problem representation and feedback on rational behavior in Allais and Morlat-type problems. Decision Sciences, 5(2), 225–242.
Savage, L.J. (1972). The foundations of statistics, 2nd edn. Dover Publications, revised republication of 1954 edition, published posthumously in 1972.
Schneider, F. H., & Schonger, M. (2019). An experimental test of the anscombe-aumann monotonicity axiom. Management Science, 65(4), 1667–1677.
Slovic, P. (1969). Differential effects of real versus hypothetical payoffs upon choices among gambles. Journal of Experimental Psychology, 80(3), 434–437.
Starmer, C. (1992). Testing new theories of choice under uncertainty using the common consequence effect. Review of Economic Studies, 59(4), 813–830.
Starmer, C., & Sugden, R. (1989). Violations of the independence axion in common ratio problems: an experimental test of some competing hypotheses. Annals of Operations Research, 19(1), 79–102.
Starmer, C., & Sugden, R. (1991). Does the random-lottery incentive system elicit true preferences? An experimental investigation. American Economic Review, 81(4), 971–978.
Wakker, P., Erev, I., & Weber, E. U. (1994). Comonotonic independence: the critical test between classical and rank-dependent utility theories. Journal of Risk and Uncertainty, 9(3), 195–230.
Wakker, P. P. (2010). Prospect theory for risk and ambiguity. New York: Cambridge University Press.
Zhou, W., & Hey, J. (2018). Context matters. Experimental Economics, 21(4), 723–756.
Acknowledgements
Thanks to John Duffy and Linda Moya, who made it possible for us to run our experiment. Many people provided us with helpful comments. Thanks especially to Dave Dillenberger, Coty Gonzales, Ed Green, Yusufcan Masatlioglu, Charles Noussair, Timonthy Shields, Peter Wakker, and workshop participants at the FUR conference, the Center for Behavioral Decision Research workshop at Carnegie Mellon, and the Society for the Advancement of Economic Theory conference. This paper originated in discussions with Horacio Arlo-Costa, and we dedicate it to his memory.
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Incekara-Hafalir, E., Kim, E. & Stecher, J.D. Is the Allais paradox due to appeal of certainty or aversion to zero?. Exp Econ 24, 751–771 (2021). https://doi.org/10.1007/s10683-020-09678-4
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DOI: https://doi.org/10.1007/s10683-020-09678-4