Violations at the Reference Point of Discontinuity: Limitations of Prospect Theory and an Alternative Model of Risk Choices

Aaron Anil Chadee, Xsitaaz T. Chadee, Clyde Chadee, Festus Otuloge


The tilted S-shaped utility function proposed in Prospect Theory (PT) relied fundamentally on the geometrical notion that there is a discontinuity between gains and losses, and that individual preferences change relative to a reference point. This results in PT having three distinct parameters; concavity, convexity and the reference point represented as a disjoint between the concavity and convexity sections of the curve. The objective of this paper is to examine the geometrical violations of PT at the zero point of reference. This qualitative study adopted a theoretical review of PT and Markowitz’s triply inflected value function concept to unravel methodological assumptions which were not fully addressed by either PT or cumulative PT. Our findings suggest a need to account for continuity and to resolve this violation of PT at the reference point. In so doing, an alternative preference transition theory, was proposed as a solution that includes a phase change space to cojoin these three separate parameters into one continuous nonlinear model. This novel conceptual model adds new knowledge of risk and uncertainty in decision making. Through a better understanding of an individual’s reference point in decision making behaviour, we add to contemporary debate by complementing empirical studies and harmonizing research in this field.


Doi: 10.28991/ESJ-2022-06-01-03

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Preferences; Prospect Theory; Value Function; Discontinuity; Transitionary Phase; Risky Choice.


Kahneman, D., & Tversky, A. (1979). Prospect Theory: An Analysis of Decision under Risk. Econometrica, 47(2), 263. doi:10.2307/1914185.

Bernheim, B. D., & Sprenger, C. (2020). On the Empirical Validity of Cumulative Prospect Theory: Experimental Evidence of Rank‐Independent Probability Weighting. Econometrica, 88(4), 1363–1409. doi:10.3982/ecta16646.

Baillon, A., Bleichrodt, H., & Spinu, V. (2020). Searching for the reference point. Management Science, 66(1), 93–112. doi:10.1287/mnsc.2018.3224.

Koszegi, B., & Rabin, M. (2007). Reference-dependent risk attitudes. American Economic Review, 97(4), 1047–1073. doi:10.1257/aer.97.4.1047.

Su, Y., & Xiong, L. (2020). A Review of Researches on the Influence of Reference Points on Newsvendor Behavior Decision. American Journal of Industrial and Business Management, 10(03), 689–697. doi:10.4236/ajibm.2020.103046.

Harel, A., Francis, J. C., & Harpaz, G. (2018). Alternative utility functions: review, analysis and comparison. Review of Quantitative Finance and Accounting, 51(3), 785–811. doi:10.1007/s11156-017-0688-z.

Pesendorfer, W. (2006). Behavioral economics comes of age: A review essay on Advances in Behavioral Economics. Journal of Economic Literature, 44(3), 712–721. doi:10.1257/jel.44.3.712.

Werner, K. M., & Zank, H. (2019). A revealed reference point for prospect theory. Economic Theory, 67(4), 731–773. doi:10.1007/s00199-017-1096-2.

Hey, J. D., & Orme, C. (2018). Investigating generalizations of expected utility theory using experimental data. Experiments in Economics: Decision Making and Markets, 62(6), 63–98. doi:10.2307/2951750.

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. doi:10.1257/jel.38.2.332.

Pinto, J. K. (2002). Project management 2002. Research Technology Management, 45(2), 22–37. doi:10.1080/08956308.2002.11671489.

Winch, G. M., & Maytorena, E. (2009). Making good sense: Assessing the quality of risky decision-making. Organization Studies, 30(2–3), 181–203. doi:10.1177/0170840608101476.

Hodgson, D., & Cicmil, S. (2016). Making projects critical 15 years on: a retrospective reflection (2001-2016). International Journal of Managing Projects in Business, 9(4), 744–751. doi:10.1108/IJMPB-10-2015-0105.

Lundin, R. A., & Midler, C. (1998). Evolution of Project as Empirical Trend and Theoretical Focus. In R. A. Lundin & C. Midler (Eds.), Projects as Arenas for Renewal and Learning Processes (pp. 1–9). Springer US. doi:10.1007/978-1-4615-5691-6_1.

Ekstedt, E., Lundin, R. A., Söderholm, A., & Wirdenius, H. (2003). Neo-industrial organising: Renewal by action and knowledge formation in a project-intensive economy. In Neo-Industrial Organising: Renewal by Action and Knowledge Formation in a Project-Intensive Economy (1st ed). Routledge. doi:10.4324/9780203360873.

Lundin, R. A., & Hartman, F. (2000). Projects as Business Constituents and Guiding Motives. In Projects as Business Constituents and Guiding Motives. Springer Science & Business Media. doi:10.1007/978-1-4615-4505-7.

J. Söderlund, P. Morris, and J. Pinto, (2012). The Oxford Handbook of Project Management. New York: Oxford University Press Inc.

Flyvbjerg, B., Holm, M. S., & Buhl, S. (2002). Underestimating costs in public works projects: Error or lie? Journal of the American Planning Association, 68(3), 279–295. doi:10.1080/01944360208976273.

Flyvbjerg, B., Ansar, A., Budzier, A., Buhl, S., Cantarelli, C., Garbuio, M., … van Wee, B. (2018). Five things you should know about cost overrun. Transportation Research Part A: Policy and Practice, 118, 174–190. doi:10.1016/j.tra.2018.07.013.

Love, P. E. D., & Ahiaga-Dagbui, D. D. (2018). Debunking fake news in a post-truth era: The plausible untruths of cost underestimation in transport infrastructure projects. Transportation Research Part A: Policy and Practice, 113, 357–368. doi:10.1016/j.tra.2018.04.019.

Love, P. E. D., Ika, L. A., & Ahiaga-Dagbui, D. D. (2019). On de-bunking ‘fake news’ in a post truth era: Why does the Planning Fallacy explanation for cost overruns fall short? Transportation Research Part A: Policy and Practice, 126, 397–408. doi:10.1016/j.tra.2019.06.013.

Chadee, A. A., Chadee, X. T., Ray, I., Mwasha, A., & Martin, H. H. (2021). When parallel schools of thought fail to converge: The case of cost overruns in project management. Buildings, 11(8), 321. doi:10.3390/buildings11080321.

Scholten, M., & Read, D. (2014). Prospect theory and the “forgotten” fourfold pattern of risk preferences. Journal of Risk and Uncertainty, 48(1), 67–83. doi:10.1007/s11166-014-9183-2.

Bouchouicha, R., & Vieider, F. M. (2017). Accommodating stake effects under prospect theory. Journal of Risk and Uncertainty, 55(1), 1–28. doi:10.1007/s11166-017-9266-y.

Georgalos, K., Paya, I., & Peel, D. A. (2021). On the contribution of the Markowitz model of utility to explain risky choice in experimental research. Journal of Economic Behavior and Organization, 182, 527–543. doi:10.1016/j.jebo.2018.11.010.

Bernoulli, D. (1954). Exposition of a New Theory on the Measurement of Risk. Econometrica, 22(1), 23. doi:10.2307/1909829.

Hey, J. D. (2005). Comparing Theories: What are We Looking for? Theory and Decision Library C:, 213–234. doi:10.1007/0-387-25706-3_13.

Mintzberg, H., & McHugh, A. (1985). Strategy formation in an adhocracy. Administrative Science Quarterly, 30(2), 160–197. doi:10.2307/2393104.

Whitley, R. (1984). the Fragmented State of Management Studies: Reasons and Consequences. Journal of Management Studies, 21(3), 331–348. doi:10.1111/j.1467-6486.1984.tb00415.x.

von Neumann, J., & Morgenstern, O. (2007). Theory of Games and Economic Behavior (60th Anniversary Commemorative Edition). Princeton University Press. doi:10.1515/9781400829460.

Stanca, L. (2020). A simplified approach to subjective expected utility. Journal of Mathematical Economics, 87, 151–160. doi:10.1016/j.jmateco.2020.01.007.

Friedman, M., & Savage, L. J. (1948). The Utility Analysis of Choices Involving Risk. Journal of Political Economy, 56(4), 279–304. doi:10.1086/256692.

Markowitz, H. (2009). The utility of wealth. Harry Markowitz: Selected Works, 60(2), 43–50. doi:10.1086/257177.

Kahneman, D., & Egan, P. (2011). Thinking, Fast and Slow (Farrar, Straus and Giroux, New York), 15.

Tversky, A., & Kahneman, D. (1992). Advances in prospect theory: Cumulative representation of uncertainty. Journal of Risk and Uncertainty, 5(4), 297–323. doi:10.1007/BF00122574.

Flyvbjerg, B. (Ed.). (2017). The Oxford handbook of megaproject management. Oxford University Press.

Quattrone, G. A., & Tversky, A. (1988). Contrasting Rational and Psychological Analyses of Political Choice. American Political Science Review, 82(3), 719–736. doi:10.2307/1962487.

Druckman, J. N. (2001). The implications of framing effects for citizen competence. Political Behavior, 23(3), 225–256. doi:10.1023/A:1015006907312.

Elms, D. K. (2004). Large Costs, Small Benefits: Explaining Trade Dispute Outcomes. Political Psychology, 25(2), 241–270. doi:10.1111/j.1467-9221.2004.00370.x.

Patty, J. W. (2006). Loss aversion, presidential responsibility, and midterm congressional elections. Electoral Studies, 25(2), 227–247. doi:10.1016/j.electstud.2005.05.004.

Herrmann, O., Jong-A-Pin, R., & Schoonbeek, L. (2019). A prospect-theory model of voter turnout. Journal of Economic Behavior and Organization, 168, 362–373. doi:10.1016/j.jebo.2019.10.012.

Levy, J. S. (1997). Prospect Theory, Rational Choice, and International Relations. International Studies Quarterly, 41(1), 87–112. doi:10.1111/0020-8833.00034.

McDermott, R. (2004). Prospect Theory in Political Science: Gains and Losses From the First Decade. Political Psychology, 25(2), 289–312. doi:10.1111/j.1467-9221.2004.00372.x.

McDermott, R., Fowler, J. H., & Smirnov, O. (2008). On the evolutionary origin of prospect theory preferences. Journal of Politics, 70(2), 335–350. doi:10.1017/S0022381608080341.

Berejikian, J. D., & Early, B. R. (2013). Loss aversion and foreign policy resolve. Political Psychology, 34(5), 649–671. doi:10.1111/pops.12012.

Wu, Y., Xu, C., & Zhang, T. (2018). Evaluation of renewable power sources using a fuzzy MCDM based on cumulative prospect theory: A case in China. Energy, 147, 1227–1239. doi:10.1016/

Hu, L., Dong, J., & Lin, Z. (2019). Modeling charging behavior of battery electric vehicle drivers: A cumulative prospect theory based approach. Transportation Research Part C: Emerging Technologies, 102, 474–489. doi:10.1016/j.trc.2019.03.027.

Ghader, S., Darzi, A., & Zhang, L. (2019). Modeling effects of travel time reliability on mode choice using cumulative prospect theory. Transportation Research Part C: Emerging Technologies, 108, 245–254. doi:10.1016/j.trc.2019.09.014.

Kühberger, A., & Schulte-Mecklenbeck, M. (2017). Theories of Economic Decision-Making: Value, Risk and Affect. Economic Psychology, 19–34. John Wiley & Sons, Ltd. doi:10.1002/9781118926352.ch2.

Takahashi, T. (2011). Psychophysics of the probability weighting function. Physica A: Statistical Mechanics and Its Applications, 390(5), 902–905. doi:10.1016/j.physa.2010.10.004.

von Neumann, J., & Morgenstern, O. (2007). Theory of Games and Economic Behavior. Princeton University Press. doi:10.2307/2981222.

Kahneman, D., & Tversky, A. (1984). Choices, values, and frames. American Psychologist, 39(4), 341–350. doi:10.1037/0003-066X.39.4.341.

Yin, R. K. (2013). Validity and generalization in future case study evaluations. Evaluation, 19(3), 321–332. doi:10.1177/1356389013497081.

Stake, R. E. (1995). The Art of Case Study Research. Thousand Oaks, CA: SAGE Publications.

Davies, A., Manning, S., & Söderlund, J. (2018). When neighboring disciplines fail to learn from each other: The case of innovation and project management research. Research Policy, 47(5), 965–979. doi:10.1016/j.respol.2018.03.002.

Cropanzano, R. (2009). Writing nonempirical articles for journal of management: General thoughts and suggestions. Journal of Management, 35(6), 1304–1311. doi:10.1177/0149206309344118.

Chung, H. K., Glimcher, P., & Tymula, A. (2018). An experimental comparison of risky and riskless choice-limitations of prospect theory and expected utility theory. American Economic Journal: Microeconomics, 11(3), 34–67. doi:10.1257/mic.20170112.

Pratt, J. W. (1978). Risk Aversion in the Small and in the Large11. This research was supported by the National Science Foundation (grant NSF-G24035). Reproduction in whole or in part is permitted for any purpose of the United States Government. Uncertainty in Economics, 59–79. doi:10.1016/b978-0-12-214850-7.50010-3.

Arrow, K. J. (1966). Exposition of the theory of choice under uncertainty. Synthese, 16(3–4), 253–269. doi:10.1007/BF00485082.

Pratt, J. W., & Zeckhauser, R. J. (1987). Proper Risk Aversion. Econometrica, 55(1), 143. doi:10.2307/1911160.

Zhang, R., Brennan, T. J., & Lo, A. W. (2014). The origin of risk aversion. Proceedings of the National Academy of Sciences of the United States of America, 111(50), 17777–17782. doi:10.1073/pnas.1406755111.

Mosteller, F., & Nogee, P. (1951). An Experimental Measurement of Utility. Journal of Political Economy, 59(5), 371–404. doi:10.1086/257106.

Coombs, C. H. (1975). Portfolio Theory and the Measurement of Risk. In H. Judgement, M. F. K. Decision Processes, & S. Schwartz (Eds.), Human Judgement and Decision Processes. Academic Press. doi:10.1016/b978-0-12-397250-7.50009-x.

Hansson, B. (1975). The appropriateness of the expected utility model. Erkenntnis, 9(2), 175–193. doi:10.1007/BF00226381.

Fishburn, P. C. (1977). Expected Utility Theories: A Review Note. In Mathematical Economics and Game Theory (pp. 197–207). Springer. doi:10.1007/978-3-642-45494-3_15.

Kahneman, D., Knetsch, J. L., & Thaler, R. H. (1991). Anomalies: The Endowment Effect, Loss Aversion, and Status Quo Bias. Journal of Economic Perspectives, 5(1), 193–206. doi:10.1257/jep.5.1.193.

Hardie, B. G. S., Johnson, E. J., & Fader, P. S. (1993). Modeling Loss Aversion and Reference Dependence Effects on Brand Choice. Marketing Science, 12(4), 378–394. doi:10.1287/mksc.12.4.378.

Camerer, C., Babcock, L., Loewenstein, G., & Thaler, R. (1997). Labor supply of New York city cabdrivers: One day at a time. Quarterly Journal of Economics, 112(2), 406–441. doi:10.1162/003355397555244.

Fehr, E., & Schmidt, K. M. (1999). A theory of fairness, competition, and cooperation. Quarterly Journal of Economics, 114(3), 817–868. doi:10.1162/003355399556151.

Genesove, D., & Mayer, C. (2001). Loss aversion and seller behavior: Evidence from the housing market. Quarterly Journal of Economics, 116(4), 1233–1260. doi:10.1162/003355301753265561.

Lindsay, L. (2013). The arguments of utility: Preference reversals in expected utility of income models. Journal of Risk and Uncertainty, 46(2), 175–189. doi:10.1007/s11166-013-9162-z.

Thaler, R. H., Tversky, A., Kahneman, D., & Schwartz, A. (1997). The effect of myopia and loss aversion on risk taking: An experimental test. Quarterly Journal of Economics, 112(2), 646–661. doi:10.1162/003355397555226.

Plott, C. R., & Zeiler, K. (2005). The willingness to pay-willingness to accept gap, the “endowment effect,” subject misconceptions, and experimental procedures for eliciting valuations. American Economic Review, 95(3), 530–545. doi:10.1257/0002828054201387.

Scholten, M., & Read, D. (2012). Anomalies to Markowitz’s Hypothesis and a Prospect-Theoretical Interpretation. SSRN Electronic Journal. doi:10.2139/ssrn.1504630.

Donkers, B., Melenberg, B., & Van Soest, A. (2001). Estimating Risk Attitudes using Lotteries: A Large Sample Approach. Journal of Risk and Uncertainty, 22(2), 165–195. doi:10.1023/A:1011109625844.

Scholten, M., Read, D., & Stewart, N. (2019). The framing of nothing and the psychology of choice. Journal of Risk and Uncertainty, 59(2), 125–149. doi:10.1007/s11166-019-09313-5.

Solow, R. M. (1956). A contribution to the theory of economic growth. Quarterly Journal of Economics, 70(1), 65–94. doi:10.2307/1884513.

Fehr-Duda, H., Bruhin, A., Epper, T., & Schubert, R. (2010). Rationality on the rise: Why relative risk aversion increases with stake size. Journal of Risk and Uncertainty, 40(2), 147–180. doi:10.1007/s11166-010-9090-0.

Levy, H., & Markowitz, H. M. (1979). Approximating expected utility by a function of mean and variance. The American Economic Review, 69(3), 308-317.

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DOI: 10.28991/ESJ-2022-06-01-03


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