Advertisement

Journal of Risk and Uncertainty

, Volume 48, Issue 1, pp 19–49 | Cite as

When Allais meets Ulysses: Dynamic axioms and the common ratio effect

  • A. Nebout
  • D. Dubois
Article
  • 377 Downloads

Abstract

We report experimental findings about subjects’ behavior in dynamic decision problems involving multistage lotteries with different timings of resolution of uncertainty. Our within-subject design allows us to study violations of the independence and dynamic axioms: Dynamic Consistency, Consequentialism and Reduction of Compound Lotteries. We investigate the effects of changes in probability and outcome levels on the pattern of choices observed in the Common Ratio Effect (CRE) and in the Reverse Common Ratio Effect (RCRE) and on their dynamic counterparts. We find that the probability level plays an important role in violations of Reduction of Compound Lottery and Dynamic Consistency and the outcomes levels in violations of Consequentialism. Moreover, more than one quarter of our subjects satisfy the Independence axiom but violate two dynamic axioms. We thus suggest that there is a greater dissociation that might have been expected between preferences captured by dynamic axioms and those observed over single-stage lotteries.

Keywords

Decision theory Experiment Independence axiom Dynamic consistency Consequentialism 

JEL Classifications

C91 D81 

Notes

Acknowledgments

This research was funded by CNRS, ANR Risk Attitude and University of Montpellier. We are grateful to Mohammed Abdellaoui, Thomas Epper, Brian Hill, John Hey, Chris Starmer, Peter Wakker and Marc Willinger, to participants in conferences in Lyon, Dijon, Barcelona and Montpellier and in seminars in Queensland University of Technology and Monash University for helpful comments. We also thank the editor and an anonymous referee for their constructive comments on earlier drafts of this paper and the managing editor, Christina Stoddard, for her great help through the entire publication process.

References

  1. Allais, M. (1953). Le comportement de l homme rationnel devant le risque : Critique des postulats et axiomes de l ecole américaine. Econometrica, 21, 503–546.CrossRefGoogle Scholar
  2. Ballinger, T.P., & Wilcox, N.T. (1997). Decisions, error and heterogeneity. The Economic Journal, 107(443), 1090–1105.CrossRefGoogle Scholar
  3. Bar-Hillel, M. (1973). On the subjective probability of compound events. Organizational Behavior and Human Performance, 9(3), 396–406.CrossRefGoogle Scholar
  4. Bardsley, N., Cubitt, R., Loomes, G., Moffat, P., Starmer, C., Sugden, R. (2010). Experimental economics: rethinking the rules. Princeton: Princeton University Press.Google Scholar
  5. Barkan, R., & Busemeyer, J.R. (2003). Modeling dynamic inconsistency with a changing reference point. Journal of Behavioral Decision Making, 16(4), 235–255.CrossRefGoogle Scholar
  6. Beattie, J., & Loomes, G. (1997). The impact of incentives upon risky choice experiments. Journal of Risk and Uncertainty, 14, 149–162.CrossRefGoogle Scholar
  7. Blavatskyy, P. (2010). Reverse common ratio effect. Journal of Risk and Uncertainty, 40, 219–241.CrossRefGoogle Scholar
  8. Bruhin, A., Fehr-Duda, H., Epper, T. (2010). Risk and rationality: uncovering heterogeneity in probability distortion. Econometrica, 78(4), 1375–1412.CrossRefGoogle Scholar
  9. Budescu, D.V., & Fischer, I. (2001). The same but different: an empirical investigation of the reducibility principle. Journal of Behavioral Decision Making, 14(3), 187–206.CrossRefGoogle Scholar
  10. Burks, A.W. (1977). Chance, cause, reason. Chicago: University of Chicago Press.Google Scholar
  11. Busemeyer, J.R., Weg, E., Barkan, R., Li, X., Ma, Z. (2000). Dynamic and consequential consistency of choices between paths of decision trees. Journal of Experimental Psychology: General, 129(4), 530–545.CrossRefGoogle Scholar
  12. Camerer, C.F., & Hogarth, R.M. (1999). The effects of financial incentives in experiments: a review and capital-labor-production framework. Journal of Risk and Uncertainty, 19, 7–42.CrossRefGoogle Scholar
  13. Carlin, P.S. (1992). Violations of the reduction and independence axioms in allais-type and common-ratio effect experiments. Journal of Economic Behavior & Organization, 19(2), 213–235.CrossRefGoogle Scholar
  14. Cubitt, R.P., Starmer, C., Sugden, R. (1998). Dynamic choice and the common ratio effect: an experimental investigation. The Economic Journal, 108(450), 1362–1380.CrossRefGoogle Scholar
  15. Hammond, P.J. (1988). Consequentialist foundations for expected utility. Theory and Decision, 25, 25–78.CrossRefGoogle Scholar
  16. Hammond, P.J. (1989). Consistent plans, consequentialism, and expected utility. Econometrica, 57(6), 1445–1449.CrossRefGoogle Scholar
  17. Hey, J., & Lee, J. (2005). Do subjects separate (or are they sophisticated)?Experimental Economics, 8(3), 233–265.CrossRefGoogle Scholar
  18. Hey, J., & Panaccione, L. (2011). Dynamic decision making: what do people do? Journal of Risk and Uncertainty, 42, 1–39.CrossRefGoogle Scholar
  19. Holt, C.A., & Laury, S. (2002). Risk aversion and incentive effects. American Economic Review, 92, 1644–1655.CrossRefGoogle Scholar
  20. Kahneman, D., & Tversky, A. (1979). Prospect theory: an analysis of decision under risk. Econometrica, 47, 263–291.CrossRefGoogle Scholar
  21. Karni, E., & Safra, Z. (1989). Dynamic consistency, revelations in auctions and the structure of preferences. The Review of Economic Studies, 56(3), 421–433.CrossRefGoogle Scholar
  22. Karni, E., & Safra, Z. (1990). Behaviorally consistent optimal stopping rules. Journal of Economic Theory, 51(2), 391–402.CrossRefGoogle Scholar
  23. Karni, E., & Schmeidler, D. (1991). Atemporal dynamic consistency and expected utility theory. Journal of Economic Theory, 54(2), 401–408.CrossRefGoogle Scholar
  24. Machina, M.J. (1989). Dynamic consistency and non-expected utility models of choice under uncertainty. Journal of Economic Literature, 27(4), 1622–1668.Google Scholar
  25. Maher, P., & Kashima, Y. (1997). Preference reversal in ellsberg problems. Philosophical Studies, 88(2), 187–207.CrossRefGoogle Scholar
  26. McClennen, E.F. (1990). Rationality and dynamic choice: foundational explorations. Cambridge: Cambridge University Press.Google Scholar
  27. McCrimmon, K., & Larsson, S. (1979). Utility theory: axioms versus paradoxes In M. Allais, & O. Hagen (Eds.), Expected utility hypotheses and the Allais paradox. D. Reidel, (pp. 27–145).Google Scholar
  28. Nebout, A. (2013). Sequential decision making without independence: a new conceptual approach. Theory and Decision, 1–26.Google Scholar
  29. Nebout, A., & Willinger, M. (2013). Are non-expected utility maximizers dynamically consistent? experimental evidence. Mimeo.Google Scholar
  30. Read, D. (2005). Monetary incentives, what are they good for? Journal of Economic Methodology, 12(2), 265–276.CrossRefGoogle Scholar
  31. Segal, U. (1987). The ellsberg paradox and risk aversion: an anticipated utility approach. International Economic Review, 28(1), 175–202.CrossRefGoogle Scholar
  32. Segal, U. (1990). Two-stage lotteries without the reduction axiom. Econometrica, 58(2), 349–77.CrossRefGoogle Scholar
  33. Starmer, C., & Sugden, R. (1989). Violations of the independence axiom in common ratio problems: an experimental test of some competing hypotheses. Annals of Operations Research, 19, 79–102.CrossRefGoogle Scholar
  34. Volij, O. (1994). Dynamic consistency, consequentialism and reduction of compound lotteries. Economics Letters, 46(2), 121–129.CrossRefGoogle Scholar
  35. von Neumann, J., & Morgenstern, O. (1947). Theory of games and economic behavior, 2nd edn. Princeton: Princeton University Press.Google Scholar
  36. Wakker, P. (1999). Justifying bayesianism by dynamic decision principles. The Netherlands: Working paper, Medical Decision Making Unit, Leiden University Medical Center.Google Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.INRA, UR1303, ALISSIvry-sur-seineFrance
  2. 2.CNRS, UMR 5474 LAMETAMontpellierFrance

Personalised recommendations