“Luce problem” and discontinuity of Prelec’s function at p = 1

Harin, Alexander (2015): “Luce problem” and discontinuity of Prelec’s function at p = 1.

Abstract

This short paper is devoted to two items: 1) An analysis of Prelec’s weighting function at the probability p = 1 is highlighted (this analysis was performed by R. Duncan Luce in two articles with Ragnar Steingrimsson and János Aczél and here is referred to as the “Luce problem”). 2) The question of possible discontinuity of Prelec’s weighting function at p = 1 is specially considered, as a manifestation of importance of the “Luce problem.”

• Item Type: MPRA Paper
• Language: English
• Keywords: Luce, Prelec; utility; prospect theory; 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; 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., & Luce, D. R. (2007). A behavioral condition for Prelec’s weighting function on the positive line without assuming W(1) = 1. Journal of Mathematical Psychology, 51, 126–129.

Chechile, R. A., & Barch, D. H. (2013). Using logarithmic derivative functions for assessing the risky weighting function for binary gambles. Journal of Mathematical Psychology, 57, 15-28.

Diecidue, E., Schmidt, U., & Zank, H. (2009). Parametric weighting functions. Journal of Economic Theory, 144, 1102–1118.

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

Harin, А. (2014). The random-lottery incentive system. Can p~1 experiments deductions be correct? 16th conference on the Foundations of Utility and Risk, (Full text http://people.few.eur.nl/baillon/be/fur2014/Harin_Alexander.pdf )

Harin, А. (2012b). Data dispersion in economics (II) – Inevitability and Consequences of Restrictions. Review of Economics & Finance, 2(4), 24–36.

Harin, А. (2012a). Data dispersion in economics (I) – Possibility of restrictions. Review of Economics & Finance, 2(3), 59–70.

Harin, А. (2007). Principle of uncertain future and utility. MPRA Paper from University Library of Munich, Germany, # 1959.

Harin, А. (2005). A Rational Irrational Man. Public Economics from EconWPA, # 0511005.

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

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

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

Steingrimsson, R., & Luce, R. D. (2007). Empirical evaluation of a model of global psychophysical judgments: IV. Forms for the weighting function. Journal of Mathematical Psychology, 51, 29–44.

Wakker, P. P. (1994). Separating Marginal Utility and Probabilistic Risk Aversion. Theory and Decision, 36, 1-44.