Problems of utility and prospect theories. Certainty effect near certainty

Harin, Alexander (2014): Problems of utility and prospect theories. Certainty effect near certainty.

Abstract

A need for experiments on the certainty effect near the certainty (near the probability p = 1) is stated in this paper. The need supported by the Aczél–Luce question whether Prelec’s weighting function W(p) is equal to 1 at p = 1, by the purely mathematical restrictions and the “certain–uncertain” inconsistency of the random–lottery incentive experiments. The results of the experiments of the certainty effect near the certainty show that Prelec’s (probability) weighting function can be discontinuous at the probability p = 1. There is a need for new experiments at probabilities which are closer to p=1, e.g., at probabilities p=.99 and p=.999.

• Item Type: MPRA Paper
• Language: English
• Keywords: utility; prospect theory; certainty effect; experiment; Prelec; probability weighting function
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General; C - Mathematical and Quantitative Methods > C9 - Design of Experiments; C - Mathematical and Quantitative Methods > C9 - Design of Experiments > C91 - Laboratory, Individual Behavior; D - Microeconomics > D8 - Information, Knowledge, and Uncertainty; D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D81 - Criteria for Decision-Making under Risk and Uncertainty

References

Aczél, J., and D. R. Luce, “A behavioral condition for Prelec’s weighting function on the positive line without assuming W(1) = 1,” Journal of Mathematical Psychology, 51 (2007), 126–129.

Allais, M., “Le comportement de l'homme rationnel devant le risque: Critique le postulats et axioms de L'École Américaine,” Econometrica, 21 (1953), 503–546.

Baltussen, G., T. Post, M. J. van den Assem, and P. P. Wakker “Random Incentive Systems in a Dynamic Choice Experiment,” Experimental Economics, 15 (2012), 418–443.

Bernoulli, D., “Specimen Theoriae Novae de Mensura Sortis,” Commentarii Academiae Scientiarum Imperialis Petropolitanae, 5 (1738), 175-192. English translation: “Exposition of a New Theory on the Measurement of Risk,” Econometrica, 22 (1954), 23–36.

Bordalo, P., N. Gennaioli, and A. Shleifer, “Salience theory of choice under risk,” The Quarterly Journal of Economics, Oxford University Press, vol. 127(3), pages 1243-1285. 2012

Butler, D., and G. Loomes, “Imprecision as an Account of the Preference Reversal Phenomenon,” American Economic Review, 97 (2007), 277–297.

Chambers, C. P., and T. Hayashi, “Preference Aggregation With Incomplete Information,” Econometrica, 82 (2014), 589–600.

Chay, K., P. McEwan, and M. Urquiola, “The Central Role of Noise in Evaluating Interventions that Use Test Scores to Rank Schools,” American Economic Review, 95 (2005), 1237–1258.

Delbaen, F., S. Drapeau, and M. Kupper, “A von Neumann–Morgenstern representation result without weak continuity assumption,” Journal of Mathematical Economics, 47 (2011), 401–408.

Ellsberg, D., “Risk, Ambiguity, and the Savage Axioms”, The Quarterly Journal of Economics, 75 (1961), 643–669.

Galaabaatar, T., and E. Karni, “Subjective Expected Utility With Incomplete Preferences,” Econometrica, 81 (2013), 255–284.

Gneezy, U., J. A. List, and G. Wu, “The Uncertainty Effect: When a Risky Prospect Is Valued Less than Its Worst Possible Outcome,” The Quarterly Journal of Economics, 121 (2006), 1283–1309.

Gul, F., and W. Pesendorfer, “Expected Uncertain Utility Theory,” Econometrica, 82 (2014), 1–40.

Halevy, Y., “Strotz Meets Allais: Diminishing Impatience and the Certainty Effect,” American Economic Review, 98 (2008), 1145–1162.

Harin, А., “The random-lottery incentive system. Can p~1 experiments deductions be correct?” 16th conference on the Foundations of Utility and Risk, 2014.

Harin, А., “Data dispersion in economics (II) – Inevitability and Consequences of Restrictions,” Review of Economics & Finance, 2 (2012), 24–36.

Harin, А., “Theorem of existence of ruptures in the probability scale,” 9th International conference “Financial and Actuarial Mathematics and Eventoconverging Technologies”, 2010.

Hey, J., and C. Orme, “Investigating Generalizations of Expected Utility Theory Using Experimental Data,” Econometrica, 62 (1994), 1291–1326.

Kahneman, D., and R. H. Thaler, “Anomalies: Utility Maximization and Experienced Utility,” Journal of Economic Perspectives, 20 (2006), 221–234.

Kahneman, D., and A. Tversky, “Prospect Theory: An Analysis of Decision under Risk,” Econometrica, 47 (1979), 263–291.

Kothiyal, A., V. Spinu, and P. P. Wakker, “Prospect theory for continuous distributions: a preference foundation,” Journal of Risk and Uncertainty, 42 (2011), 195–210.

McCord, M., and R. de Neufville, “Lottery Equivalents: Reduction of the Certainty Effect Problem in Utility Assessment,” Management Science, 32 (1986), 56–60.

Neumann Von, J., and O. Morgenstern, Theory of games and economic behavior, 2nd ed. Princeton, NJ: Princeton University Press, 1947.

Prelec, D., “The Probability Weighting Function,” Econometrica, 66 (1998), 497–527.

Schoemaker, P., The Expected Utility Model: Its Variants, Purposes, Evidence and LimitationsAuthor(s): Paul J. H. Schoemaker Source: Journal of Economic Literature, Vol. 20, No. 2 (Jun., 1982), pp. 529–563

Schoemaker, P., and J. Hershey, “Utility measurement: Signal, noise, and bias,” Organizational Behavior and Human Decision Processes, 52 (1992), 397–424.

Spinu, V., and P. P. Wakker, “Expected Utility without Continuity: A Comment on Delbaen, Drapeau, and Kupper (2011),” Journal of Mathematical Economics, 49 (2013), 28–30.

Starmer, C., “Developments in Non-Expected Utility Theory: The Hunt for a Descriptive Theory of Choice under Risk,” Journal of Economic Literature, 38 (2000), 332–382.

Starmer, C., and R. Sugden, “Does the Random-Lottery Incentive System Elicit True Preferences? An Experimental Investigation,” American Economic Review, 81 (1991), 971–78.

Tversky, A, and D. Kahneman (1992): "Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, 5, 297–323.

Tversky, A., and P. P. Wakker, “Risk attitudes and decision weights,” Econometrica, 63 (1995), 1255–1280.