Abstract
The paper addresses decision making with imperfect information and suggests simple techniques for handling uncertainties in the framework of the Kahneman and Tversky prospects theory using methods of subjective beliefs governed by uninorm and absorbing norm aggregators. The suggested method utilizes observations that people assign higher probabilities to predictions, which have either high or low probabilities and lower probabilities to the predictions with intermediate probabilities, and usually prefer avoiding choice to other alternatives. The method is verified by direct application to the original experimental results presented by Kahneman and Tversky. In addition, it is demonstrated that the suggested model completely coincides both with the recent Enke and Graeber model of cognitive uncertainty and with the conventional model based on the Shannon entropy and provides a unified framework for both techniques. In the discussion section, the paper addresses the inferences of the suggested method in the economic studies.
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Code Availability
The MATLAB® scripts of the suggested operators and presented calculations are available and can be provided for free for any non-commercial purposes.
References
Von Neumann J, Morgenstern O (1944) Theory of Games and Economic Behavior. Princeton University Press, Princeton
Friedman M, Savage L (1948) The utility analysis of choices involving risks. J Political Economy 56:279–304
Kahneman D, Tversky A (1979) Prospect theory: an analysis of decision under risk. Econometrica 47(2):263–292
Tversky A, Kahneman D (1992) Prospect theory: cumulative representation of uncertainty. J Risk and Uncertainty 5:297–323
Aliev R, Huseynov O (2014) Decision Theory with Imperfect Information. World Scientific, Singapore
Batyrshin I, Kaynak O, Rudas I (2002) Fuzzy Modeling Based on Generalized Conjunction Operations. IEEE Trans Fuzzy Systems 10(5):678–683
Kagan E, Rybalov A, Siegelmann H, Yager R (2013) Probability-generated aggregators Int J Intelligent Systems 28:709–727
Kagan E. Rybalov A, Yager R (2020) Subjective Markov process with fuzzy aggregations. In Proc. 12th Int. Conf. Agents and Artificial Intelligence, Valletta
Rybalov A, Kagan E, Yager R (2012) Parameterized uninorm and absorbing norm and their application for logic design. In Proc IEEE Conv EEEI Eilat
Yager R, Rybalov A (1996) Uninorm aggregation operators. Fuzzy Sets Syst 80:111–120
Ruggeri K, Ali S, Berge ML et al (2020) Replicating patterns of prospect theory for decision under risk. Nature Human Behavior 4:622–633
Fodor J, Yager R, Rybalov A (1997) Structure of uninorms. Int J Uncertainty, Fuzziness and Knowledge-Based Systems 5:411–427
Fodor J, Rudas I, Bede B (2004) Uninorms and absorbing norms with applications to image processing. In Proc SISY 59–72
Enke B, Graeber T (2019) Cognitive uncertainty. NBER Working Paper Series
Raiffa H (1968) Decision analysis. Introductory lectures on choices under uncertainty. Random House, New York
Cover T, Thomas J (1991) Elements of information theory. John Wiley & Sons, Chichester
Kézdi G, Willis R (2011) Household stock market beliefs and learning. NBER Working Paper 17614
Pan Y, Siegel S, Wang TY (2014) The cultural origin of preferences: CEO Cultural Heritage and Corporate Investment. Working Paper, University of Utah
Epper T, Fehr-Duda H, Bruhin A (2011) Viewing the future through a warped lens: Why uncertainty generates hyperbolic discounting. J Risk and Uncertainty 43(3):169–203
Pfeffer J, Hardisty D (2017) Intertemporal uncertainty avoidance: when the future is uncertain, people prefer the present, and when the present is uncertain, people prefer the future. Manage Sci 63(2):519–527
Thaler R (1981) Some empirical evidence on dynamic inconsistency. Econ Lett 8:201–207
Acknowledgements
We sincerely thank the reviewer for kind notice of the research by Dr. Tomas Folke; the experiments conducted by Dr. Folke and his collaborators on a wide range of respondents from different countries completely support the results by Kahneman and Tversky and allow considering their conclusions as proven facts.
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Kagan, E., Rybalov, A. Subjective Trusts and Prospects: Some Practical Remarks on Decision Making with Imperfect Information. Oper. Res. Forum 3, 19 (2022). https://doi.org/10.1007/s43069-022-00129-9
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DOI: https://doi.org/10.1007/s43069-022-00129-9