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Mean, Median or Mode? A Striking Conclusion From Lottery Experiments

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  • Kontek, Krzysztof

Abstract

This paper deals with estimating data from experiments determining lottery certainty equivalents. The paper presents the parametric and nonparametric results of the least squares (mean), quantile (including median) and mode estimations. The examined data are found to be positively skewed for low probabilities and negatively skewed for high probabilities. This observation leads to the striking conclusion that lottery valuations are only nonlinearly related to probability when means are considered. Such nonlinearity is not confirmed by the mode estimator in which case the most likely lottery valuations are close to their expected values. This means that the most likely behavior of a group is fully rational. This conclusion is a significant departure from one of the fundamental results concerning lottery experiments presented so far.

Suggested Citation

  • Kontek, Krzysztof, 2010. "Mean, Median or Mode? A Striking Conclusion From Lottery Experiments," MPRA Paper 21758, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:21758
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    File URL: https://mpra.ub.uni-muenchen.de/21758/1/MPRA_paper_21758.pdf
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    References listed on IDEAS

    as
    1. Lee, Myoung-jae, 1989. "Mode regression," Journal of Econometrics, Elsevier, vol. 42(3), pages 337-349, November.
    2. 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.
    3. Krzysztof Kontek, 2009. "Lottery valuation using the aspiration / relative utility function," Working Papers 39, Department of Applied Econometrics, Warsaw School of Economics.
    4. Ulrich Schmidt & Stefan Traub, 2009. "An Experimental Investigation of the Disparity Between WTA and WTP for Lotteries," Theory and Decision, Springer, vol. 66(3), pages 229-262, March.
    5. Kontek, Krzysztof, 2009. "Absolute vs. Relative Notion of Wealth Changes," MPRA Paper 17336, University Library of Munich, Germany.
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    Cited by:

    1. Kontek, Krzysztof, 2010. "Multi-Outcome Lotteries: Prospect Theory vs. Relative Utility," MPRA Paper 22947, University Library of Munich, Germany.
    2. Kontek, Krzysztof, 2010. "Density Based Regression for Inhomogeneous Data: Application to Lottery Experiments," MPRA Paper 22268, University Library of Munich, Germany.

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    More about this item

    Keywords

    Lottery experiments; Least Squares; Quantile; Median; and Mode Estimators; Nonparametric and Parametric Estimators; Relative Utility Function; Prospect Theory.;
    All these keywords.

    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • C91 - Mathematical and Quantitative Methods - - Design of Experiments - - - Laboratory, Individual Behavior
    • D03 - Microeconomics - - General - - - Behavioral Microeconomics: Underlying Principles
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C81 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Methodology for Collecting, Estimating, and Organizing Microeconomic Data; Data Access
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • D87 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Neuroeconomics

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