×

Second-best probability weighting. (English) Zbl 1508.91179

Summary: Non-linear probability weighting is an integral part of descriptive theories of choice under risk such as prospect theory. But why do these objective errors in information processing exist? Should we try to help individuals overcome their mistake of overweighting small and underweighting large probabilities? In this paper, we argue that probability weighting can be seen as a compensation for preexisting biases in evaluating payoffs. In particular, inverse S-shaped probability weighting is a flipside of S-shaped payoff valuation. Probability distortions may thus have survived as a second-best solution to a fitness maximization problem, and it can be counter-productive to correct them while keeping the value function unchanged.

MSC:

91B16 Utility theory

References:

[1] Acemoglu, D., Yildiz, M., 2001. Evolution of perception and play. Mimeo.
[2] Baliga, S.; Ely, J., Mnemonomics: the sunk cost fallacy as a memory kludge, Am. Econ. J. Microecon., 3, 35-67 (2011)
[3] Bergstrom, T., 1997. Storage for good times and bad: of rats and men. Mimeo.
[4] Bernardo, A.; Welch, I., On the evolution of overconfidence and entrepreneurs, J. Econ. Manag. Strategy, 10, 301-330 (2001)
[5] Berns, G.; Capra, C.; Chappelow, J.; Moore, S.; Noussair, C., Nonlinear neurobiological probability weighting functions for aversive outcomes, NeuroImage, 39, 2047-2057 (2008)
[6] Besharov, G., Second-best considerations in correcting cognitive biases, South. Econ. Rev., 71, 12-20 (2004)
[7] Bénabou, R.; Tirole, J., Self-confidence and personal motivation, Q. J. Econ., 117, 871-915 (2002) · Zbl 1037.91082
[8] Brocas, I.; Carrillo, J., Entrepreneurial boldness and excessive investment, J. Econ. Manag. Strategy, 13, 321-350 (2004)
[9] Bruhin, A.; Fehr-Duda, H.; Epper, T., Risk and rationality: uncovering heterogeneity in probability distortion, Econometrica, 78, 1375-1412 (2010) · Zbl 1232.91121
[10] Camerer, C.; Issacharoff, S.; Loewenstein, G.; O’Donoghue, T., Regulation for conservatives: behavioral economics and the case for “asymmetric paternalism”, Univ. Pa. Law Rev., 151, 1211-1254 (2003)
[11] Camerer, C.; Lovallo, D., Overconfidence and excess entry: an experimental approach, Am. Econ. Rev., 89, 306-318 (1999)
[12] Carrillo, J.; Mariotti, T., Strategic ignorance as a self-disciplining device, Rev. Econ. Stud., 67, 529-544 (2000) · Zbl 1055.91508
[13] Compte, O.; Postlewaite, A., Confidence-enhanced performance, Am. Econ. Rev., 94, 1536-1557 (2004)
[14] Cooper, S.; Kaplan, R., Adaptive “coin-flipping”: a decision-theoretic examination of natural selection for random individual variation, J. Theor. Biol., 94, 135-151 (1982)
[15] Curry, P., Decision making under uncertainty and the evolution of interdependent preferences, J. Econ. Theory, 98, 357-369 (2001) · Zbl 0985.91017
[16] Dillenberger, D.; Postlewaite, D.; Rozen, K., Optimism and pessimism with expected utility, J. Eur. Econ. Assoc., 15, 1158-1175 (2017)
[17] Dobbs, I.; Molho, I., Evolution and sub-optimal behavior, J. Evol. Econ., 9, 187-209 (1999)
[18] Efthimiou, C., 2010. Introduction to Functional Equations. MSRI mathematical circles library.
[19] Ely, J., Kludged, Am. Econ. J. Microecon., 3, 210-231 (2011)
[20] Enke, B., Graeber, T., 2021. Cognitive uncertainty. Mimeo.
[21] Fehr-Duda, H.; Bruhin, A.; Epper, T.; Schubert, R., Rationality on the rise: why relative risk aversion increases with stake size, J. Risk Uncertain., 40, 2, 147-180 (2010)
[22] Frenkel, S.; Heller, Y.; Teper, R., The endowment effect as blessing, Int. Econ. Rev., 59, 1159-1186 (2018) · Zbl 1417.91176
[23] Friedman, D., The s-shaped value function as a constrained optimum, Am. Econ. Rev., 79, 1243-1248 (1989)
[24] Friedman, D.; Massaro, D. W., Understanding variability in binary and continuous choice, Psychon. Bull. Rev., 5, 3, 370-389 (1998)
[25] Gonzalez, R.; Wu, G., On the shape of the probability weighting function, Cogn. Psychol., 38, 129-166 (1999)
[26] Hamo, Y., Heifetz, A., 2002. An evolutionary perspective on goal seeking and s-shaped utility. Mimeo.
[27] Heifetz, A.; Shannon, C.; Spiegel, Y., The dynamic evolution of preferences, Econ. Theory, 32, 2, 251-286 (2007) · Zbl 1137.91006
[28] Hsu, M.; Krajbich, I.; Zhao, C.; Camerer, C., Neural response to reward anticipation under risk is nonlinear in probabilities, J. Neurosci., 18, 2231-2237 (2009)
[29] Johnson, D.; Fowler, J., The evolution of overconfidence, Nature, 477, 317-320 (2011)
[30] Kahneman, D.; Lovallo, D., Timid choices and bold forecasts: a cognitive perspective on risk taking, Manag. Sci., 39, 17-31 (1993)
[31] Kahneman, D.; Tversky, A., Prospect theory: an analysis of decision under risk, Econometrica, 47, 263-291 (1979) · Zbl 0411.90012
[32] Karmarkar, U., Subjectively weighted utility: a descriptive extension of the expected utility model, Organ. Behav. Hum. Perform., 21, 61-72 (1978)
[33] Karmarkar, U., Subjectively weighted utility and the Allais paradox, Organ. Behav. Hum. Perform., 24, 67-72 (1979)
[34] Kornienko, T., 2011. A cognitive basis for context-dependent utility. Mimeo.
[35] Lipsey, R.; Lancaster, K., The general theory of second best, Rev. Econ. Stud., 24, 11-32 (1956)
[36] Maynard Smith, J., Optimization theory in evolution, Annu. Rev. Ecol. Syst., 9, 31-56 (1978)
[37] McDermott, R.; Fowler, J.; Smirnov, O., On the evolutionary origin of prospect theory preferences, J. Polit., 70, 335-350 (2008)
[38] Netzer, N., Evolution of time preferences and attitudes toward risk, Am. Econ. Rev., 99, 937-955 (2009)
[39] Netzer, N., Robson, A., Steiner, J., Kocourek, P., 2021. Endogenous risk attitudes. Mimeo.
[40] Noeldeke, G.; Samuelson, L., Information-based relative consumption effects: correction, Econometrica, 73, 1383-1387 (2005) · Zbl 1151.91603
[41] Parker, G. A.; Maynard Smith, J., Optimality theory in evolutionary biology, Nature, 348, 27-33 (1990)
[42] Platt, M.; Glimcher, P. W., Neural correlates of decision variables in parietal cortex, Nature, 400, 233-238 (1999)
[43] Prelec, D., The probability weighting function, Econometrica, 66, 497-527 (1998) · Zbl 1009.91007
[44] Qiu, J.; Steiger, E.-M., Understanding the two components of risk attitudes: an experimental analysis, Manag. Sci., 57, 193-199 (2011)
[45] Quiggin, J., A theory of anticipated utility, J. Econ. Behav. Organ., 3, 323-343 (1982)
[46] Rayo, L.; Becker, G., Evolutionary efficiency and happiness, J. Polit. Econ., 115, 302-337 (2007)
[47] Rieger, M., Evolutionary stability of prospect theory preferences, J. Math. Econ., 50, 1-11 (2014) · Zbl 1284.91049
[48] Rieger, M.; Wang, M.; Hens, T., Prospect theory around the world (2011), SSRN Working Paper No. 1957606
[49] Robson, A., A biological basis for expected and non-excpected utility, J. Econ. Theory, 68, 397-424 (1996) · Zbl 0852.90019
[50] Robson, A., The biological basis of economic behavior, J. Econ. Lit., 39, 11-33 (2001)
[51] Robson, A.; Samuelson, L., The evolution of time preference with aggregate uncertainty, Am. Econ. Rev., 99, 1925-1953 (2009)
[52] Robson, A.; Samuelson, L., The evolutionary foundations of preferences, (Bisin, A.; Jackson, M., Handbook of Social Economics (2010), North-Holland), 221-310
[53] Robson, A.; Samuelson, L., The evolution of decision and experienced utilities, Theor. Econ., 6, 311-339 (2011) · Zbl 1279.91055
[54] Samuelson, L., Information-based relative consumption effects, Econometrica, 72, 93-118 (2004) · Zbl 1151.91604
[55] Samuelson, L.; Swinkels, J., Information, evolution and utility, Theor. Econ., 1, 119-142 (2006)
[56] Shafer, W., The nontransitive consumer, Econometrica, 42, 913-919 (1974) · Zbl 0291.90007
[57] Sharot, T.; Riccardi, A.; Raio, C.; Phelps, E., Neural mechanisms mediating optimism bias, Nature, 450, 102-196 (2007)
[58] Steiner, J.; Stewart, C., Perceiving prospects properly, Am. Econ. Rev., 106, 1601-1631 (2016)
[59] Suzuki, T., Complementarity of behavioral biases, Theory Decis., 72, 413-430 (2012) · Zbl 1242.91051
[60] Tobler, P.; Christopoulos, G.; O’Doherty, J.; Dolan, R.; Schultz, W., Neuronal distortions of reward probability without choice, J. Neurosci., 28, 11703-11711 (2008)
[61] Tom, S.; Fox, C.; Trepel, C.; Poldrack, R., The neural basis of loss aversion in decision-making under risk, Science, 315, 515-518 (2007)
[62] Tversky, A.; Kahneman, D., Advances in prospect theory: cumulative representation of uncertainty, J. Risk Uncertain., 5, 297-323 (1992) · Zbl 0775.90106
[63] Waldman, M., Systematic errors and the theory of natural selection, Am. Econ. Rev., 84, 482-497 (1994)
[64] Wolpert, D.; Leslie, D., Information theory and observational limitations in decision making, B. E. J. Theor. Econ., 12 (2012) · Zbl 1277.91040
[65] Woodford, M., 2012a. Inattentive valuation and reference-dependent choice. Mimeo.
[66] Woodford, M., Prospect theory as efficient perceptual distortion, Am. Econ. Rev. Pap. Proc., 102, 3, 41-46 (2012)
[67] Yao, J.; Li, D., Bounded rationality as a source of loss aversion and optimism: a study of psychological adaptation under incomplete information, J. Econ. Dyn. Control, 37, 18-31 (2013) · Zbl 1345.91003
[68] Zhang, H., Evolutionary justifications for non-Bayesian beliefs, Econ. Lett., 121, 198-201 (2013) · Zbl 1288.91022
[69] Zhong, S.; Israel, S.; Xue, H.; Ebstein, R.; Chew, S., Monoamine oxidase a gene (maoa) associated with attitude towards longshot risks, PLoS ONE, 4, 12, Article e8516 pp. (2009)
[70] Zhong, S.; Israel, S.; Xue, H.; Sham, P.; Ebstein, R.; Chew, S., A neurochemical approach to valuation sensitivity over gains and losses, Proc. R. Soc. Lond. B, Biol. Sci., 276, 4181-4188 (2009)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.