Harin, Alexander (2018): Forbidden zones for the expectation of a random variable. New version 1.

PDF
MPRA_paper_84248.pdf Download (248kB)  Preview 
Abstract
A forbidden zones theorem is deduced in the present article. Its consequences and applications are preliminary considered. The following statement is proven: if some nonzero lower bound exists for the variance of a random variable, that takes on values in a finite interval, then nonzero bounds or forbidden zones exist for its expectation near the boundaries of the interval. The article is motivated by the need of rigorous theoretical support for the practical analysis that has been performed for the influence of scattering and noise in the behavioral economics, decision sciences, utility and prospect theories. If a noise can be one of possible causes of the above lower bound on the variance, then it can cause or broaden out such forbidden zones. So the theorem can provide new possibilities for mathematical description of the influence of such a noise. The considered forbidden zones can evidently lead to some biases in measurements.
Item Type:  MPRA Paper 

Original Title:  Forbidden zones for the expectation of a random variable. New version 1 
Language:  English 
Keywords:  probability; variance; noise; utility theory; prospect theory; behavioral economics; decision sciences; measurement; 
Subjects:  C  Mathematical and Quantitative Methods > C0  General > C02  Mathematical Methods C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General D  Microeconomics > D8  Information, Knowledge, and Uncertainty D  Microeconomics > D8  Information, Knowledge, and Uncertainty > D81  Criteria for DecisionMaking under Risk and Uncertainty 
Item ID:  84248 
Depositing User:  Alexander Harin 
Date Deposited:  29 Jan 2018 20:23 
Last Modified:  04 Oct 2019 05:01 
References:  Aczél, J., and D. R. Luce, "A behavioral condition for Prelec’s weighting function on the positive line without assuming W(1)=1", Journal of Mathematical Psychology, 51 (2007), 126–129. Butler, David, and Graham Loomes, “Imprecision as an Account of the Preference Reversal Phenomenon,” American Economic Review, 97 (2007), 277297. Chay, K., P. McEwan, and M. Urquiola, “The Central Role of Noise in Evaluating Interventions that Use Test Scores to Rank Schools”, American Economic Review, 95 (2005), 12371258. Dokov, S. P., Morton, D.P., 2005. SecondOrder Lower Bounds on the Expectation of a Convex Function. Math. Oper. Res. 30(3), 662–677. Harin, A., 2007, “Principle of uncertain future, examples of its application in economics, potentials of its applications in theories of complex systems, in set theory, probability theory and logic”, Seventh International Scientific School "Modelling and Analysis of Safety and Risk in Complex Systems", 2007. Harin, A., 2012a, “Data dispersion in economics (I) – Possibility of restrictions,” Review of Economics & Finance, 2 (2012), 5970. Harin, A., 2012b, “Data dispersion in economics (II) – Inevitability and Consequences of Restrictions,” Review of Economics & Finance, 2 (2012), 2436. Harin, А. 2013, Data dispersion near the boundaries: can it partially explain the problems of decision and utility theories? Working Papers from HAL No. 00851022, 2013. Harin, A., 2014a, “The randomlottery incentive system. Can p~1 experiments deductions be correct?” 16th conference on the Foundations of Utility and Risk, 2014. Harin, A., 2014b, “Partially unforeseen events. Corrections and correcting formulae for forecasts,” Expert Journal of Economics, 2(2) (2014), 69–79. Harin, A., 2015. General bounds in economics and engineering at data dispersion and risk, Proceedings of the Thirteenth International Scientific School 13, 105–117, in Modeling and Analysis of Safety and Risk in Complex Systems (SaintPetersburg: IPME RAS). Harin, А. 2016, An inconsistency between certain outcomes and uncertain incentives within behavioral methods, MPRA Paper No. 75311, 2016. Harin, А. 2017, Can forbidden zones for the expectation explain noise influence in behavioral economics and decision sciences? MPRA Paper No. 76240, 2017. Hey, J., and C. Orme, “Investigating Generalizations of Expected Utility Theory Using Experimental Data,” Econometrica, 62 (1994), 12911326. Kahneman, D., and Thaler, R., 2006. Anomalies: Utility Maximization and Experienced Utility, J Econ. Perspect. 20(1), 221–234. Kahneman, D., and A. Tversky, “Prospect Theory: An Analysis of Decision under Risk,” Econometrica, 47 (1979), 263291. Pinelis, I., 2011. Exact lower bounds on the exponential moments of truncated random variables, J Appl. Probab. 48(2), 547–560. Prékopa, A., 1990, The discrete moment problem and linear programming, Discrete Appl. Math. 27(3), 235–254. Prékopa, A., 1992. Inequalities on Expectations Based on the Knowledge of Multivariate Moments. Shaked M, Tong YL, eds., Stochastic Inequalities, 309–331, number 22 in Lecture NotesMonograph Series (Institute of Mathematical Statistics). Prelec, Drazen, “The Probability Weighting Function,” Econometrica, 66 (1998), 497527. Schoemaker, P., and J. Hershey, “Utility measurement: Signal, noise, and bias,” Organizational Behavior and Human Decision Processes, 52 (1992), 397424. Steingrimsson, R., and R. D. Luce, “Empirical evaluation of a model of global psychophysical judgments: IV. Forms for the weighting function,” Journal of Mathematical Psychology, 51 (2007), 29–44. Thaler, R., 2016. Behavioral Economics: Past, Present, and Future, American Economic Review. 106(7), 1577–1600. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/84248 