Abstract
In situations when we know the probabilities of all possible consequences, traditional decision theory recommends selecting the action that maximizes expected utility. In many practical situations, however, we only have partial information about the corresponding probabilities. In this case, for different possible probability distributions, we get different values of expected utility. In general, possible values of expected utility form an interval. One way to approach this situation is to use the optimism-pessimism approach proposed by Nobelist Leo Hurwicz. Another approach is to select one of the possible probability distributions – e.g., the one that has the largest possible entropy. Both approaches have led to many good practical applications. Usually, we get reasonable conclusions even when we ignore some of the available information – e.g., because this information is too vague to be easily formalized. In this paper, we show, on the example of the two envelopes problem, that ignoring available information can lead to counter-intuitive recommendations.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Fishburn, P.C.: Utility Theory for Decision Making. Wiley, New York (1969)
Hurwicz, L.: Optimality Criteria for Decision Making Under Ignorance. Cowles Commission Discussion Paper, Statistics, No. 370 (1951)
Jaynes, E.T., Bretthorst, G.L.: Probability Theory: The Logic of Science. Cambridge University Press, Cambridge (2003)
Kahneman, D.: Thinking, Fast and Slow, Farrar, Straus, and Giroux, New York (2011)
Kosheleva, O., Afravi, M., Kreinovich, V.: Why utility non-linearly depends on money: a commonsense explanation. In: Proceedings of the 4th International Conference on Mathematical and Computer Modeling, Omsk, Russia, 11 November 2016, pp. 13–18 (2016)
Kreinovich, V.: Decision making under interval uncertainty (and beyond). In: Guo, P., Pedrycz, W. (eds.) Human-Centric Decision-Making Models for Social Sciences, pp. 163–193. Springer, Heidelberg (2014)
Lorkowski, J., Kreinovich, V.: Granularity helps explain seemingly irrational features of human decision making. In: Pedrycz, W., Chen, S.-M. (eds.) Granular Computing and Decision-Making: Interactive and Iterative Approaches, pp. 1–31. Springer, Cham (2015)
Luce, R.D., Raiffa, R.: Games and Decisions: Introduction and Critical Survey. Dover, New York (1989)
McDonnell, M.D., Abott, D.: Randomized switching in the two-envelope problem. Proc. Roy. Soc. A 465(2111), 3309–3322 (2009)
Nguyen, H.T., Kosheleva, O., Kreinovich, V.: Decision making beyond Arrow’s ‘impossibility theorem’, with the analysis of effects of collusion and mutual attraction. Int. J. Intell. Syst. 24(1), 27–47 (2009)
Nguyen, H.T., Kreinovich, V., Wu, B., Xiang, G.: Computing Statistics under Interval and Fuzzy Uncertainty. Springer, Heidelberg (2012)
Raiffa, H.: Decision Analysis. McGraw-Hill, Columbus (1997)
Acknowledgments
This work was supported in part by the National Science Foundation grants 1623190 (A Model of Change for Preparing a New Generation for Professional Practice in Computer Science) and HRD-1242122 (Cyber-ShARE Center of Excellence).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Bokati, L., Kosheleva, O., Kreinovich, V. (2021). It Is Important to Take All Available Information into Account When Making a Decision: Case of the Two Envelopes Problem. In: Allahviranloo, T., Salahshour, S., Arica, N. (eds) Progress in Intelligent Decision Science. IDS 2020. Advances in Intelligent Systems and Computing, vol 1301. Springer, Cham. https://doi.org/10.1007/978-3-030-66501-2_34
Download citation
DOI: https://doi.org/10.1007/978-3-030-66501-2_34
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-66500-5
Online ISBN: 978-3-030-66501-2
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)