Nonparametric numerical approaches to probability weighting function construct for manifestation and prediction of risk preferences
Abstract
Probability weighting function (PWF) is the psychological probability of a decision-maker for objective probability, which reflects and predicts the risk preferences of decision-maker in behavioral decisionmaking. The existing approaches to PWF estimation generally include parametric methodologies to PWF construction and nonparametric elicitation of PWF. However, few of them explores the combination of parametric and nonparametric elicitation approaches to approximate PWF. To describe quantitatively risk preferences, the Newton interpolation, as a well-established mathematical approximation approach, is introduced to task-specifically match PWF under the frameworks of prospect theory and cumulative prospect theory with descriptive psychological analyses. The Newton interpolation serves as a nonparametric numerical approach to the estimation of PWF by fitting experimental preference points without imposing any specific parametric form assumptions. The elaborated nonparametric PWF model varies in accordance with the number of the experimental preference points elicitation in terms of its functional form. The introduction of Newton interpolation to PWF estimation into decision-making under risk will benefit to reflect and predict the risk preferences of decision-makers both at the aggregate and individual levels. The Newton interpolation-based nonparametric PWF model exhibits an inverse S-shaped PWF and obeys the fourfold pattern of decision-makers’ risk preferences as suggested by previous empirical analyses.
First published online 17 April 2023
Keyword : probability weighting function, risk preference, nonparametric numerical approach, Newton interpolation, preference points, decision-making under risk
How to Cite
Wu, S., Chen, Z.-S., Pedrycz, W., Govindan, K., & Chin, K.-S. (2023). Nonparametric numerical approaches to probability weighting function construct for manifestation and prediction of risk preferences. Technological and Economic Development of Economy, 29(4), 1127–1167. https://doi.org/10.3846/tede.2023.18551
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
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Bleichrodt, H., & Pinto, J. L. (2000). A parameter-free elicitation of the PWF in medical decision analysis. Management Science, 46(11), 1485–1496. https://doi.org/10.1287/mnsc.46.11.1485.12086
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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. https://doi.org/10.1007/BF01065371
Carnahan, B., Luther, H. A., & Wilkes, J. O. (1969). Applied numerical methods. Wiley New York. https://doi.org/10.1002/aic.690160604
Cavagnaro, D. R., Pitt, M. A., Gonzalez, R., & Myung, J. I. (2013). Discriminating among PWFs using adaptive design optimization. Journal of Risk and Uncertainty, 47(3), 255–289. https://doi.org/10.1007/s11166-013-9179-3
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Chen, Z.-S., Zhang, X., Rodriguez, R. M., Pedrycz, W., Martinez, L., & Skibniewski, M. J. (2022). Expertise-structure and risk-appetite-integrated two-tiered collective opinion generation framework for large scale group decision making. IEEE Transactions on Fuzzy Systems, 30(12), 5496–5510. https://doi.org/10.1109/TFUZZ.2022.3179594
Croson, R., & Gneezy, U. (2009). Gender differences in preferences. Journal of Economic Literature, 47(2), 448–474. https://doi.org/10.1257/jel.47.2.448
Diecidue, E., Schmidt, U., & Zank, H. (2009). Parametric weighting functions. Journal of Economic Theory, 144(3), 1102–1118. https://doi.org/10.1016/j.jet.2008.10.004
Farquhar, P. H. (1984). State of the art – Utility assessment methods. Management Science, 30(11), 1283–1300. https://doi.org/10.1287/mnsc.30.11.1283
Gonzalez, R. (1993). Estimating the weighting function [Conference presentation]. 26th Annual Mathematical Psychology Meeting.
Gonzalez, R., & Wu, G. (1999). On the shape of the PWF. Cognitive Psychology, 38(1), 129–166. https://doi.org/10.1006/cogp.1998.0710
Hershey, J. C., & Schoemaker, P. J. (1985). Probability versus certainty equivalence methods in utility measurement: Are they equivalent? Management Science, 31(10), 1213–1231. https://doi.org/10.1287/mnsc.31.10.1213
Hong, C. S., & Waller, W. S. (1986). Empirical tests of weighted utility theory. Journal of Mathematical Psychology, 30(1), 55–72. https://doi.org/10.1016/0022-2496(86)90042-8
Huang, Y., Lin, R., & Chen, X. (2021). An enhancement EDAS method based on prospect theory. Technological and Economic Development of Economy, 27(5), 1019–1038. https://doi.org/10.3846/tede.2021.15038
Jiang, W. H., Xu, L., Chen, Z. S., Govindan, K., & Chin, K. S. (2022). Financing equilibrium in a capital constrained supply Chain: The impact of credit rating. Transportation Research Part E: Logistics and Transportation Review, 157, 102559. https://doi.org/10.1016/j.tre.2021.102559
Kahneman, D., & Tversky, A. (1979). Prospect theory: An analysis of decision under risk. Econometrica, 47(2), 263–291. https://doi.org/10.2307/1914185
Kahneman, D., & Tversky, A. (1984). Choices, values, and frames. American Psychologist, 39(4), 341–350. https://doi.org/10.1037/0003-066X.39.4.341
Kilka, M., & Weber, M. (2001). What determines the shape of the PWF under uncertainty? Management Science, 47(12), 1712–1726. https://doi.org/10.1287/mnsc.47.12.1712.10239
Krzysztofowicz, R. (1983). Strength of preference and risk attitude in utility measurement. Organizational Behavior and Human Performance, 31(1), 88–113. https://doi.org/10.1016/0030-5073(83)90114-9
Kahneman, D., & Tversky, A. (2013). Prospect theory: An analysis of decision under risk. In World scientific handbook in financial economics series: Vol. 4. Handbook of the fundamentals of financial decision making: Part I (pp. 99–127). World Scientific. https://doi.org/10.1142/9789814417358_0006
Lattimore, P. K., Baker, J. R., & Witte, A. D. (1992). The influence of probability on risky choice: A parametric examination. Journal of Economic Behavior and Organization, 17(3), 377–400. https://doi.org/10.1016/S0167-2681(95)90015-2
Luce, R. D., & Fishburn, P. C. (1991). Rank- and sign-dependent linear utility models for finite first-order gambles. Journal of Risk and Uncertainty, 4(1), 29–59. https://doi.org/10.1007/BF00057885
Petrova, D. G., Pligt, J., & Garcia-Retamero, R. (2014). Feeling the numbers: On the interplay between risk, affect, and numeracy. Journal of Behavioral Decision Making, 27(3), 191–199. https://doi.org/10.1002/bdm.1803
Prelec, D. (1998) The Probability Weighting Function. Econometrica, 66(3), 497–527. https://doi.org/10.2307/2998573
Rieger, M. O., Wang, M., & Hens, T. (2015). Risk preferences around the world. Management Science, 61(3), 637–648. https://doi.org/10.1287/mnsc.2013.1869
Roussanov, N., & Savor, P. (2014). Marriage and managers’ attitudes to risk. Management Science, 60(10), 2496–2508. https://doi.org/10.1287/mnsc.2014.1926
Ruggeri, K., Alí, S., Berge, M. L., Bertoldo, G., Bjørndal, L. D., Cortijos-Bernabeu, A., Davison, C., Demić, E., Esteban-Serna, C., Friedemann, M., Gibson, S. P., Jarke, H., Karakasheva, R., Khorrami, P. R., Kveder, J., Andersen, T. L., Lofthus, I. S., McGill, L., Nieto, A. E., … Folke, T. (2020). Replicating patterns of prospect theory for decision under risk. Nature Human Behaviour, 4, 622–633. https://doi.org/10.1038/s41562-020-0886-x
Schmidt, U., & Zank, H. (2005). What is loss aversion? Journal of Risk and Uncertainty, 30(2), 157–167. https://doi.org/10.1007/s11166-005-6564-6
Scholten, M., & Read, D. (2014). Prospect theory and the “forgotten” fourfold pattern of risk preferences. Journal of Risk and Uncertainty, 48(1), 67–83. https://doi.org/10.1007/s11166-014-9183-2
Starmer, C. (2000). Developments in non-expected utility theory: The hunt for a descriptive theory of choice under risk. Journal of Economic Literature, 38(2), 332–382. https://doi.org/10.1257/jel.38.2.332
Stewart, N., Reimers, S., & Harris, A. J. (2015). On the origin of utility, weighting, and discounting functions: How they get their shapes and how to change their shapes. Management Science, 61(3), 687–705. https://doi.org/10.1287/mnsc.2013.1853
Tanaka, T., Camerer, C. F., & Nguyen, Q. (2010). Risk and time preferences: Linking experimental and household survey data from Vietnam. American Economic Review, 100(1), 557–571. https://doi.org/10.1257/aer.100.1.557
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