Harin, Alexander (2013): A nonzero dispersion leads to the nonzero bias of mean.

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Abstract
A theorem of existence of the nonzero restrictions for the mean of a function on a finite numerical segment at a nonzero dispersion of the function is proved. The theorem has an applied character. It is aimed to be used in the probability theory and statistics and further in economics. Its ultimate aim is to help to answer the AczélLuce question whether W(1)=1 and to explain, at least partially, the wellknown problems and paradoxes of the utility theory, such as the underweighting of high and the overweighting of low probabilities, the Allais paradox, the fourfold pattern paradox, etc., by purely mathematical methods.
Item Type:  MPRA Paper 

Original Title:  A nonzero dispersion leads to the nonzero bias of mean 
Language:  English 
Keywords:  utility; utility theory; probability; uncertainty; decisions; economics; Prelec; probability weighting; Allais paradox; risk aversion; 
Subjects:  C  Mathematical and Quantitative Methods > C0  General 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 > D81  Criteria for DecisionMaking under Risk and Uncertainty G  Financial Economics > G2  Financial Institutions and Services > G22  Insurance ; Insurance Companies ; Actuarial Studies 
Item ID:  47559 
Depositing User:  Alexander Harin 
Date Deposited:  11 Jun 2013 17:04 
Last Modified:  27 Sep 2019 00:56 
References:  [1] Bernoulli D. (1738), “Specimen Theoriae Novae de Mensura Sortis”, Commentarii Academiae Scientiarum Imperialis Petropolitanae, 5 (1738): 175192. English translation: “Exposition of a New Theory on the Measurement of Risk”, Econometrica, 22(1): 2336. [2] Allais, M. (1953) Le comportement de l'homme rationnel devant le risque: Critique le postulats et axioms de L'École Américaine. Econometrica, 21: 503546. [3] Ellsberg L. (1961), “Risk, Ambiguity, and the Savage Axioms”, The Quarterly Journal of Economics, 75 (4): 643669. [4] Tversky, A. and Wakker, P. (1995) Risk attitudes and decision weights. Econometrica, 63: 12551280. [5] Kahneman, D. and Thaler, R. (2006) "Anomalies: Utility Maximization and Experienced Utility" Journal of Economic Perspectives, 20, #1: 221234. [6] Hey, J., and Orme C. (1994), “Investigating Generalizations of Expected Utility Theory Using Experimental Data”, Econometrica, 62 (6): 12911326. [7] Chay, K., McEwan, P., and Urquiola M. (2005), “The Central Role of Noise in Evaluating Interventions that Use Test Scores to Rank Schools”, American Economic Review, 95 (4): 12371258. [8] Butler, D. J., and Loomes G. C. (2007), “Imprecision as an Account of the Preference Reversal Phenomenon”, American Economic Review, 97 (1): 277297. [9] Aczél, János and R. Duncan Luce (2006), “A behavioral condition for Prelec’s weighting function on the positive line without assuming W(1)=1” Journal of Mathematical Psychology. Volume 51, Issue 2, April 2007, Pages 126–129. [10] Harin А. (2009), “About existence of ruptures in the probability scale: Calculation of ruptures’ values”, Proceedings of the Ninth International Scientific School "Modelling and Analysis of Safety and Risk in complex systems", 9, 458464, (2009) (in Russian). [11] Harin А. (2010), “Theorem of existence of ruptures in the probability scale”, Proceedings of the 9th International conference "Financial and Actuarial Mathematics and Eventoconverging Technologies", 9, 312315, (2010) (in Russian). [12] Harin А. (2012), “Economics. Paradoxes. Ruptures. Eventology”, Proceedings of the 11th International conference "Financial and Actuarial Mathematics and Eventology of Safety", 11, 368371, (2012) (in Russian). 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/47559 