Harin, Alexander (2015): Is Prelec’s function discontinuous at p = 1? (for the Einhorn Award of SJDM).

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Abstract
A possibility of the existence of a discontinuity of Prelec’s (probability weighting) function at the probability p = 1 is discussed. This possibility is supported by the purely mathematical theorems and the “certain–uncertain” inconsistency of the random–lottery incentive experiments. The results of the wellknown experiment support it as well.
Item Type:  MPRA Paper 

Original Title:  Is Prelec’s function discontinuous at p = 1? (for the Einhorn Award of SJDM) 
Language:  English 
Keywords:  Prelec; utility; prospect theory; probability weighting function; Luce; 
Subjects:  C  Mathematical and Quantitative Methods > C0  General C  Mathematical and Quantitative Methods > C0  General > C02  Mathematical Methods C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General C  Mathematical and Quantitative Methods > C8  Data Collection and Data Estimation Methodology ; Computer Programs C  Mathematical and Quantitative Methods > C9  Design of Experiments C  Mathematical and Quantitative Methods > C9  Design of Experiments > C91  Laboratory, Individual Behavior C  Mathematical and Quantitative Methods > C9  Design of Experiments > C93  Field Experiments D  Microeconomics > D0  General > D01  Microeconomic Behavior: Underlying Principles D  Microeconomics > D8  Information, Knowledge, and Uncertainty D  Microeconomics > D8  Information, Knowledge, and Uncertainty > D81  Criteria for DecisionMaking under Risk and Uncertainty G  Financial Economics > G0  General > G02  Behavioral Finance: Underlying Principles G  Financial Economics > G1  General Financial Markets > G11  Portfolio Choice ; Investment Decisions 
Item ID:  64672 
Depositing User:  Alexander Harin 
Date Deposited:  28. May 2015 23:16 
Last Modified:  28. May 2015 23:18 
References:  Abdellaoui, M., A. Baillon, L. Placido, and P. P. Wakker, “The Rich Domain of Uncertainty: Source Functions and Their Experimental Implementation,” American Economic Review, 101 (2011), 695–723. Abramowitz, M. and Stegun, I. eds., Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, New York: Dover Publications (1972). 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. Andreoni, J., and C. Sprenger, “Risk Preferences Are Not Time Preferences,” American Economic Review, 102 (2012), 3357–76. 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. Beattie, J., and G. Loomes, “The impact of incentives upon risky choice experiments,” Journal of Risk and Uncertainty, 14 (1997), 155–168. Bordalo, P., N. Gennaioli, and A. Shleifer, “Salience theory of choice under risk,” The Quarterly Journal of Economics, 127 # 3, (2012), 12431285. Butler, D., and G. Loomes, “Imprecision as an Account of the Preference Reversal Phenomenon,” American Economic Review, 97 (2007), 277–297. Chechile, R. A., and D. H. Barch, “Using logarithmic derivative functions for assessing the risky weighting function for binary gambles,” Journal of Mathematical Psychology, 57 (2013), 1528. Cubitt, R., C. Starmer, and R. Sugden, “On the validity of the random lottery incentive system,” Experimental Economics, 1 (1998), 115–131. Diecidue, E., U. Schmidt, and H. Zank, “Parametric weighting functions,” Journal of Economic Theory, 144 (2009), 1102–1118. 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., “An existence theorem for restrictions on the mean in the presence of a restriction on the dispersion,” MPRA Paper, Item ID: 64646, (2015). Harin, А., “The randomlottery incentive system. Can p~1 experiments deductions be correct?” 16th conference on the Foundations of Utility and Risk, )2014). Harin, А., 2012b, “Data dispersion in economics (II) – Inevitability and Consequences of Restrictions,” Review of Economics & Finance, 2 (November 2012), 24–36. Harin, А., 2012a, “Data dispersion in economics (I) – Possibility of restrictions,” Review of Economics & Finance, 2 (August 2012), 5970. Harin, А., “Ruptures in the probability scale? Calculation of ruptures’ dimensions,” MPRA Paper, Item ID: 19348, (2009). Harrison, G. W., E. Johnson, M. Mcinnes, and E. Rutström, “Risk Aversion and Incentive Effects: Comment,” American Economic Review, 95 (2005), 897–901. Holt, C. A., and S. K. Laury, “Risk Aversion and Incentive Effects” American Economic Review, 92 (2002), 1644–1655. Kahneman, D., J. L. Knetsch, and R. H. Thaler, “Anomalies: The Endowment Effect, Loss Aversion, and Status Quo Bias,” The Journal of Economic Perspectives, 5 (1991), 193–206. 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. Larkin, I., and S. Leider, “Incentive Schemes, Sorting, and Behavioral Biases of Employees: Experimental Evidence,” American Economic Journal: Microeconomics, 4 (2012), 184–214. Loewenstein, G., and R. H. Thaler, “Anomalies. Intertemporal Choice,” Journal of Economic Perspectives, 3 (1989), 181–193. Masson, R. T., “Utility Functions with Jump Discontinuities: Some Evidence and Implications from Peasant Agriculture,” Economic Inquiry, 12 (1974), 559–566. Prelec, D., “The Probability Weighting Function,” Econometrica, 66 (1998), 497–527. Schoemaker, P., “The Expected Utility Model: Its Variants, Purposes, Evidence and Limitations,” Journal of Economic Literature, 20, # 2 (1982), 529–563 Schoemaker, P., and J. Hershey, “Utility measurement: Signal, noise, and bias,” Organizational Behavior and Human Decision Processes, 52 (1992), 397–424. Steingrimsson, R., and R. D. Luce, “Empirical evaluation of a model of global psychophysical judgments: IV. Forms for the weighting function,” Journal of Mathematical Psychology, 51 (2007), 29–44. Starmer, C., “Developments in NonExpected 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 RandomLottery Incentive System Elicit True Preferences? An Experimental Investigation,” American Economic Review, 81 (1991), 971–78. Tversky, A, and D. Kahneman, “Advances in Prospect Theory: Cumulative Representation of Uncertainty,” Journal of Risk and Uncertainty, 5 (1992), 297–323. Tversky, A., and P. P. Wakker, “Risk attitudes and decision weights,” Econometrica, 63 (1995), 1255–1280. Vossler, C. A., M. Doyon, and D. Rondeau, “Truth in Consequentiality: Theory and Field Evidence on Discrete Choice Experiments,” American Economic Journal: Microeconomics, 4 (2012), 145–171. Wakker, P.P., “Separating marginal utility and probabilistic risk aversion,” Theory and Decision, 36 (1994) 144. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/64672 