Prospect Theory

The subjectively expected utility theory is theoretically dominant in the science of decision-making for a long time. However, Kahneman and Tversky (1979) which is really a vastly influential paper in economics after over thirty years of publication[1] shows that this theoretical prevalence is not always consistently right, particularly under the experimental settings and also introduces an elegantly alternative approach of analysis for making decisions in uncertainty, that is called prospect theory. This essay aims to critically review prospect theory from existing literature. Particularly, summaries of theory with comparisons with the subjectively expected utility theory, the evolutionary process, key contributions, highlighting applications, and challenges facing the theory in moving further in literature of making decisions under risk and uncertainty are presented.

Prospect theory is always referred in comparison with the subjectively expected utility theory because of not only they are all dominantly crucial theories of choices under risk and uncertainty but also prospect theory was raised from drawbacks of the canonical counterpart (Sebora and Cornwall 1995), particularly in terms of three key hypotheses including the preference consistency, the linearity of weighting decisions, and the point of reference for making decisions. Regarding the consistency of preferences, the subjectively expected utility theory assumes that people’s preference on outcomes is consistent and not affected by the context, i.e the modes of presenting alternatives. Hence people are completely able to rank alternatives in accordance with their subjective ordering and choose the best one which is help them maximize their utility (Kahneman and Tversky 1984). In contrast, in prospect theory preference is indicated by decision makers because the ability to choose alternative is accordingly influenced by psychological effects stemming from the manner of presenting outcomes, the context as well as bounded rationality (Simon 1985). Particularly, Kahneman and Tversky (1979) model a process of making decisions with two stages including editing and evaluation chronologically. For the first stage, decision makers fundamentally analyse given different prospects facing them by conducting some important operations such as coding, combination, segregation, and cancellation. Subsequently, the highest value among edited prospects which are analysed in the first stage is chosen as a final decision of decision-makers.

In consideration of the linearity of decision weights, the subjectively expected utility model employs probabilities of occurrence to assign to possible outcomes to determine the value of an alternative in a linear function. The alternative with highest value of utility is chosen by rationally unbounded decision makers. Adversely, prospect theory points out that the value of utilities is a function of decision weights which are non-linear. Specifically, Kahneman and Tversky (1979) evidently theorize the tendency that people usually underweight highly possible outcomes while adversely overweight outcomes with low possibilities.[2] Manifestly, prospect theory challengingly violates a profoundly key principle of the subjectively expected utility theory in the manner of weighting decisions. Moreover, prospect theory also introduced outcomes with non-monetary values in addition to monetary outcomes from the expected utility theory.

In terms of the reference point for making decisions, the subjectively expected utility theory assumes that people aims only to maximize their utilities of final states of outcomes or assets and totally do not concern gains or losses from any point for making reference during the process of making decisions. In doing this, its utility function is defined over the final outcomes and the point of reference does become neutrality. Furthermore, the expected utility theory assumes that the utility function is consistently concave under any setting of environment which is the solidly fundamental foundation for risk aversion. In violation of the subjectively expected utility theory, prospect theory fundamentally focuses on the losses and gains relative to the reference point instead of the final states of wealth. Apparently the subjectively expected utility theory is seriously flawed without explanations of changing people’s utility due to gains or losses during the process of making decisions. Additionally, prospect theory characterizes that when making decisions dis-utilities due to losses of wealth or assets is larger the counterparts from gaining which is called loss aversion. Specifically, Kahneman and Tversky (1979) show that risk aversion is psychologically an inconsistent phenomena facing people when they make decisions under different setting of prospects.[3] Particularly, people show risk aversion in the prospect of gains and inversely risk-seeking in the domain of losses. Apparently, this reflection effect evidently broken the fundamental of expected utility theory and lunched the definition of loss aversion instead of risk aversion in the experimental environment. Although there are many differences, both theories are also same in the method to calculate the value of alternatives from the choice set of decision makers. Particularly, the value is mathematically the result of summed products of specific outcomes and corresponding probabilities assigned to them.[4]

Prospect theory is successively developed with many generations since the first original one (Kahneman and Tversky 1979). Subsequently, the modified version of “original” prospect theory that is cumulative prospect theory is viewed as the second generation of this theory (Tversky and Kahneman 1992). This version of prospect theory notably characterizes the tenet of decisions weighting with being rank-dependent (Tversky and Kahneman 1992; Wakker and Tversky 1993). Currently the third generation is introduced with a specially augmented version with important some extensions including uncertain reference points and specified decision weights which is developed from previous version of prospect theory (Schmidt, Starmer and Sugden 2008).

Prospect theory provides distinctively massive contributions. Most importantly it marks an achievement of attempting to incorporate psychology into economics and other social sciences to study behavioural choice making under risk and uncertain conditions (Camerer 2005; List 2004).[5] The evolution of prospect theory obviously plays massive roles in the development of behavioural economics in the context of poorly predictions from neo-classical economics to sketch human actions with more reality (Camerer 2005). Indeed, prospect theory is theoretically incorporated into many models in economics as well as other social sciences to dramatically and impressively move the literature in theory of making decisions forward and empirically tested by many applied researchers (Barberis 2013). For instance, loss aversion can significantly and sensitively explain the St. Petersburg paradox (Camerer 2005).

Over three last decades, applications of prospect theory has widely spanned within many subfields of economics (Camerer 2000; DellaVigna 2009; Kahneman 2011; Barberis 2013).[6] Specifically, there are such applications in the study of dynamic household consumptions (Kőszegi and Rabin 2009), industrial organization (Kőszegi and Rabin 2006), labour economics (Camerer, Babcock, Loewenstein, and Thaler 1997; Crawford and Meng 2011), health economics (Happich and Mazurek 2002), and environmental economics (Rosenman, Fort and Budd 1988). Especially, in behavioural finance, prospect theory is applied in asset prices (Barberis and Huang 2008; Barberis, Huang, and Santos 2001), cross-sectional average returns (Conrad, Dittmar, and Ghysels 2013), dynamic trading of financial assets (Genesove and Mayer 2001), and the disposition effect in stock markets (Barberis and Xiong 2012). Meanwhile, the study of insurance consists of insurance choices (Barseghyan, Molinari, O’Donoghue, and Teitelbaum 2013), insurance expectations (Kőszegi and Rabin 2007), or “annuitization puzzles” (Hu and Scott 2007).

Despite the fact that prospect theory is fruitfully growingly applied in economics as well as other social sciences, it still faces some remarkable challenges (Barberis 2013). Firstly, because prospect theory does not take into account for aspects of disappointments and regret which often exist in the real world, it does not explain what subsequently happen when there are changes from the preference point (Kahneman 2011). Although prospect theory therefore move the theory of decision making on further to the real world, it is not complete. Secondly, prospect theory is an excellently analytical framework for making decisions under risk in experimental settings however Barberis (2013) argues that the difficulties of application prevented prospect theory from widespread applications outside experimental settings.

In summary, arguments in this essay indicate that remarkably important differences in approaches to the preference consistency, the linearity of weighting decisions, and the point of reference compared to the subjectively expected utility theory make prospect theory becomes increasingly dominant alternative for the study of making decision under risk and uncertainty. Prospect theory growingly contributes to research in economics as well as other social sciences since the publication of Kahneman and Tversky (1979) and potentially have further developments and applications in future.

References

Avineri, Erel and Caspar G. Chorus. 2010. “Editorial: Recent Developments in Prospect Theory-based Travel Behaviour Research.” European Journal of Transport and Infrastructure Research 10(4): 293–298.

Barberis, Nicholas C. 2013. “Thirty Years of Prospect Theory in Economics: A Review and Assessment.” Journal of Economic Perspectives 27(1): 173–196.

Barberis, Nicholas, and Ming Huang. 2008. “Stocks as Lotteries: The Implications of Probability Weighting for Security Prices.” American Economic Review 98(5): 2066–2100.

Barberis, Nicholas, and Wei Xiong. 2012. “Realization Utility.” Journal of Financial Economics 104(2): 251–71.

Barberis, Nicholas, Ming Huang and Tano Santos. 2001. “Prospect Theory and Asset Prices.” Quarterly Journal of Economics 116(1): 1–53.

Barseghyan, Levon, Francesca Molinari, Ted O'Donoghue, and Joshua C. Teitelbaum. 2013. "The Nature of Risk Preferences: Evidence from Insurance Choices." American Economic Review 103(6): 2499–2529.

Camerer, Colin F. 2000. “Prospect Theory in the Wild: Evidence from the Field.” In Choices, Values and Frames, edited by Daniel Kahneman and Amos Tversky. Cambridge University Press.

Camerer, Colin, Linda Babcock, George Loewenstein, and Richard Thaler. 1997. “Labor Supply of New York City Cabdrivers: One Day at a Time.” Quarterly Journal of Economics 112(2): 407–441.

Camerer, Colin. 2005. “Three Cheers–Psychological, Theoretical, Empirical–For Loss Aversion.” Journal of Marketing Research 42(2): 129–133.

Conrad, Jennifer, Robert F. Dittmar, and Eric Ghysels. 2013. “Ex Ante Skewness and Expected Stock Returns.” The Journal of Finance 68(1): 85–124.

Crawford, Vincent, and Juanjuan Meng. 2011. “New York City Cab Drivers’ Labor Supply Revisited: Reference-Dependent Preferences with Rational-Expectations Targets for Hours and Income.” American Economic Review 101(5): 1912–32.

DellaVigna, Stefano. 2009. “Psychology and Economics: Evidence from the Field.” Journal of Economic Literature 47(2): 315–72.

Genesove, David, and Christopher Mayer. 2001. “Loss Aversion and Seller Behavior: Evidence from the Housing Market.” Quarterly Journal of Economics 116(4): 1233–60.

Happich, H. and B. Mazurek. 2002. “Priorities and Prospect Theory.” The European Journal of Health Economics 3(1): 40–46.

Hu, Wei-Yin, and Jason S. Scott. 2007. “Behavioral Obstacles in the Annuity Market.” Financial Analysts Journal 63(6): 71– 82.

Kahneman, Daniel, and Amos Tversky. 1979. “Prospect Theory: An Analysis of Decision under Risk.” Econometrica 47(2): 263–91.

Kahneman, Daniel, and Amos Tversky. 1984. "Choices, Values, and Frames." American Psychologist 39: 341–350.

Kahneman, Daniel. 2011. Thinking, Fast and Slow. New York: Farrar, Straus, and Giroux.

Kőszegi, Botond, and Matthew Rabin. 2006. “A Model of Reference-Dependent Preferences.” Quarterly Journal of Economics 121(4): 1133–65.

Kőszegi, Botond, and Matthew Rabin. 2007. “Reference-Dependent Risk Attitudes.” American Economic Review 97(4): 1047–73.

Kőszegi, Botond, and Matthew Rabin. 2009. “Reference-Dependent Consumption Plans.” American Economic Review 99(3): 909–36.

Levy, Jack S. 1992. “An Introduction to Prospect Theory.” Political Psychology 13(2): 171–186.

Levy, Jack S. 2003. “Applications of Prospect Theory to Political Science.” Synthese 135(2): 215–241.

List, John A. 2004. “Neoclassical Theory versus Prospect Theory: Evidence from the Marketplace.” Econometrica 72(2): 615–625.

Markowitz, Harry. 1952. “The Utility of Wealth.” Journal of Political Economy 60: 151–158.

Rosenman, Robert, Rodney Fort and William Budd. 1988. “Perceptions, Fear, and Economic Loss: An Application of Prospect Theory to Environmental Decision Making.” Policy Sciences 21(4): 327–350.

Royal Swedish Academy of Sciences (2002). “The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 2002: Daniel Kahneman, Vernon L. Smith.” Press Release. http://nobelprize.org/nobel_prizes/economics/laureates/2002/press.html

Sebora, Terrence C. and Jeffrey R. Cornwall. 1995. “Expected Utility Theory Vs. Prospect Theory: Implications For Strategic Decision Makers.” Journal of Managerial Issues 1: 41–61.

Simon, Herbert. 1985. “Human Nature in Politics: The Dialogue of Psychology with Political Science.” American Political Science Review 79(2): 293–304.

Tversky, Amos, and Daniel Kahneman. 1992. “Advances in Prospect Theory: Cumulative Representation of Uncertainty.” Journal of Risk and Uncertainty 5(4): 297–323.

Ulrich Schmidt & Chris Starmer & Robert Sugden 2008. Third-generation prospect theory. Journal of Risk and Uncertainty 36:203–223.

Wakker, Peter P., and Amos Tversky. 1993. “An Axiomatization of Cumulative Prospect Theory.” Journal of Risk and Uncertainty 7: 147–176.

Yuping Liu. 1998. “Prospect Theory: Developments and Applications in Marketing.” Working Paper #98-01. http://www.yupingliu.com/files/papers/liu_prospect_theory.pdf

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[1] There are approximately nearly 30,000 citations for this paper by the time of this essay written from the Google Scholars.

[2] This is indicated as the certainty effect.

[3] This is called the reflection effect.

[4] The mathematical formula is , where v(x) is the utility of a specific outcome among n outcomes, and w(p) is the corresponding probability which is weighted for that outcome.

[5] Daniel Kahneman, jointly with  Vernon L. Smith, honourly awarded the Bank of Sweden Prize in Economic Sciences in Memory of Alfred Nobel in 2002 “for having integrated insights from psychological research into economic science, especially concerning human judgment and decision-making under uncertainty” (Royal Swedish Academy of Sciences 2002).

[6] Additionally, prospect theory has widely been applied in other social sciences such as transportations (Avineri and Chorus 2010), international relations (Levy 1992), political science (Levy 2003), marketing (Liu 1998), and management (Sebora and Cornwall 1995).