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Forbidden zones for the expectation. New mathematical results for behavioral and social sciences

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  • Harin, Alexander

Abstract

A forbidden zones theorem, mathematical approach and model are proposed in the present article. In particular, the approach supposes that people decide as if there were some biases of the expectations of measurement data. The article is motivated by the need of a theoretical support for the practical analysis performed for the purposes of utility and prospect theories, behavioral economics, psychology, decision and social sciences. Possible general consequences and applications of the theorem and approach for a noise and biases of measurement data are preliminary considered as well.

Suggested Citation

  • Harin, Alexander, 2018. "Forbidden zones for the expectation. New mathematical results for behavioral and social sciences," MPRA Paper 86650, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:86650
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    File URL: https://mpra.ub.uni-muenchen.de/86650/1/MPRA_paper_86650.pdf
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    References listed on IDEAS

    as
    1. Alexander Harin, 2012. "Data Dispersion in Economics (I) - Possibility of Restrictions," Review of Economics & Finance, Better Advances Press, Canada, vol. 2, pages 59-70, August.
    2. repec:eee:spapps:v:127:y:2017:i:7:p:2262-2280 is not listed on IDEAS
    3. Alexander Harin, 2013. "Data dispersion near the boundaries: can it partially explain the problems of decision and utility theories?," Working Papers hal-00851022, HAL.
    4. Tversky, Amos & Kahneman, Daniel, 1992. "Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 297-323, October.
    5. John D. Hey & Chris Orme, 2018. "Investigating Generalizations Of Expected Utility Theory Using Experimental Data," World Scientific Book Chapters,in: Experiments in Economics Decision Making and Markets, chapter 3, pages 63-98 World Scientific Publishing Co. Pte. Ltd..
    6. Kenneth Y. Chay & Patrick J. McEwan & Miguel Urquiola, 2005. "The Central Role of Noise in Evaluating Interventions That Use Test Scores to Rank Schools," American Economic Review, American Economic Association, vol. 95(4), pages 1237-1258, September.
    7. Horst, Ulrich & Hu, Ying & Imkeller, Peter & Réveillac, Anthony & Zhang, Jianing, 2014. "Forward–backward systems for expected utility maximization," Stochastic Processes and their Applications, Elsevier, vol. 124(5), pages 1813-1848.
    8. James Cox & Vjollca Sadiraj & Ulrich Schmidt, 2015. "Paradoxes and mechanisms for choice under risk," Experimental Economics, Springer;Economic Science Association, vol. 18(2), pages 215-250, June.
    9. Starmer, Chris & Sugden, Robert, 1991. "Does the Random-Lottery Incentive System Elicit True Preferences? An Experimental Investigation," American Economic Review, American Economic Association, vol. 81(4), pages 971-978, September.
    10. Harin, Alexander, 2017. "Can forbidden zones for the expectation explain noise influence in behavioral economics and decision sciences?," MPRA Paper 76240, University Library of Munich, Germany.
    11. Daniel Ellsberg, 1961. "Risk, Ambiguity, and the Savage Axioms," The Quarterly Journal of Economics, Oxford University Press, vol. 75(4), pages 643-669.
    12. Scheutzow, Michael, 1985. "Noise can create periodic behavior and stabilize nonlinear diffusions," Stochastic Processes and their Applications, Elsevier, vol. 20(2), pages 323-331, September.
    13. Alexander Harin, 2012. "Data Dispersion in Economics(II) - Inevitability and Consequences of Restrictions," Review of Economics & Finance, Better Advances Press, Canada, vol. 2, pages 24-36, November.
    14. Kahneman, Daniel & Tversky, Amos, 1979. "Prospect Theory: An Analysis of Decision under Risk," Econometrica, Econometric Society, vol. 47(2), pages 263-291, March.
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    16. Steftcho P. Dokov & David P. Morton, 2005. "Second-Order Lower Bounds on the Expectation of a Convex Function," Mathematics of Operations Research, INFORMS, vol. 30(3), pages 662-677, August.
    17. Daniel Kahneman & Richard H. Thaler, 2006. "Anomalies: Utility Maximization and Experienced Utility," Journal of Economic Perspectives, American Economic Association, vol. 20(1), pages 221-234, Winter.
    18. Nicholas C. Barberis, 2013. "Thirty Years of Prospect Theory in Economics: A Review and Assessment," Journal of Economic Perspectives, American Economic Association, vol. 27(1), pages 173-196, Winter.
    19. Xie, Bin, 2016. "Some effects of the noise intensity upon non-linear stochastic heat equations on [0,1]," Stochastic Processes and their Applications, Elsevier, vol. 126(4), pages 1184-1205.
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    More about this item

    Keywords

    probability; variance; noise; bias; measurement; utility theory; prospect theory; behavioral economics; psychology; decision sciences; social sciences;

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • D8 - Microeconomics - - Information, Knowledge, and Uncertainty
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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