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Inequalities and zones. New mathematical results for behavioral and social sciences

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  • Harin, Alexander

Abstract

A theorem, mathematical method and model are introduced in the present article. Inequalities, allowed and forbidden zones, their relations, consequences, and applications are considered for the expectations of random variables. The method and model are based on the inequalities and zones of the theorem. The article is motivated by the need for theoretical support for the practical analysis performed for the purposes of behavioral economics.

Suggested Citation

  • Harin, Alexander, 2018. "Inequalities and zones. New mathematical results for behavioral and social sciences," MPRA Paper 90326, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:90326
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    File URL: https://mpra.ub.uni-muenchen.de/90326/1/MPRA_paper_90326.pdf
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    References listed on IDEAS

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    1. 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.
    2. David J. Butler & Graham C. Loomes, 2007. "Imprecision as an Account of the Preference Reversal Phenomenon," American Economic Review, American Economic Association, vol. 97(1), pages 277-297, March.
    3. 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..
    4. Drazen Prelec, 1998. "The Probability Weighting Function," Econometrica, Econometric Society, vol. 66(3), pages 497-528, May.
    5. 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.
    6. Harin, Alexander, 2018. "Forbidden zones for the expectation. New mathematical results for behavioral and social sciences," MPRA Paper 86650, University Library of Munich, Germany.
    7. Richard H. Thaler, 2016. "Behavioral Economics: Past, Present, and Future," American Economic Review, American Economic Association, vol. 106(7), pages 1577-1600, July.
    8. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    9. 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.
    10. 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.
    11. Schoemaker, Paul J. H. & Hershey, John C., 1992. "Utility measurement: Signal, noise, and bias," Organizational Behavior and Human Decision Processes, Elsevier, vol. 52(3), pages 397-424, August.
    12. 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.
    13. R. Sharma & R. Bhandari, 2014. "On Variance Upper Bounds for Unimodal Distributions," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 43(21), pages 4503-4513, November.
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    Citations

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    Cited by:

    1. Harin, Alexander, 2019. "Forbidden zones for the expectations of measurement data and problems of behavioral economics," MPRA Paper 91368, University Library of Munich, Germany.
    2. Alexander Harin, 2022. "Forbidden Zones for the Expectations of Data: New Mathematical Methods and Models for Behavioral Economics," Academic Journal of Applied Mathematical Sciences, Academic Research Publishing Group, vol. 8(1), pages 12-26, 12-2021.
    3. Alexander Harin, 2024. "About a “Certain-uncertain†Inconsistency within the Generally Accepted Experimental Procedures of Behavioral Economics," International Journal of Economics and Financial Research, Academic Research Publishing Group, vol. 10(2), pages 17-30, 06-2024.
    4. Harin, Alexander, 2020. "Macroscopic analogs of quantum-mechanical phenomena and auto-transformations of functions," MPRA Paper 104188, University Library of Munich, Germany.
    5. Harin, Alexander, 2020. "Behavioral sciences and auto-transformations of functions," MPRA Paper 99286, University Library of Munich, Germany.
    6. Alexander Harin, 2021. "Auto-Transformations of the Probability Density Functions," Academic Journal of Applied Mathematical Sciences, Academic Research Publishing Group, vol. 7(3), pages 167-178, 07-2021.
    7. Harin, Alexander, 2021. "Behavioral economics. Forbidden zones. New method and models," MPRA Paper 106545, University Library of Munich, Germany.
    8. Harin, Alexander, 2019. "Behavioral sciences and auto-transformations. Introduction," MPRA Paper 97344, University Library of Munich, Germany.

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    More about this item

    Keywords

    probability; variance; noise; bias; measurement; utility theory; prospect theory; behavioral economics; psychology; social sciences;
    All these keywords.

    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
    • D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations

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