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Moral Impossibility in the Petersburg Paradox : A Literature Survey and Experimental Evidence

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  • Tibor Neugebauer

    (Luxembourg School of Finance, University of Luxembourg)

Abstract

The Petersburg paradox has led to much thought for three centuries. This paper describes the paradox, discusses its resolutions advanced in the literature while alluding to the historical context, and presents experimental data. In particular, Bernoulli’s search for the level of moral impossibility in the Petersburg problem is stressed; beyond this level small probabilities are considered too unlikely to be relevant for judgment and decision making. In the experiment, the level of moral impossibility is elicited through variations of the gamble-length in the Petersburg gamble. Bernoulli’s conjecture that people neglect small probability events is supported by a statistical power analysis.

Suggested Citation

  • Tibor Neugebauer, 2010. "Moral Impossibility in the Petersburg Paradox : A Literature Survey and Experimental Evidence," LSF Research Working Paper Series 10-14, Luxembourg School of Finance, University of Luxembourg.
    • Handle: RePEc:crf:wpaper:10-14
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    References listed on IDEAS

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    1. Marc Rieger & Mei Wang, 2006. "Cumulative prospect theory and the St. Petersburg paradox," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 28(3), pages 665-679, August.
    2. Sinn, Hans-Werner, 1980. "Ökonomische Entscheidungen bei Ungewißheit," Monograph, Mohr Siebeck, Tübingen, edition 1, number urn:isbn:9783169427024.
    3. Gilbert W. Bassett, Jr., 1987. "The St. Petersburg Paradox and Bounded Utility," History of Political Economy, Duke University Press, vol. 19(4), pages 517-523, Winter.
    4. James C. Cox & Vjollca Sadiraj, 2008. "Risky Decisions in the Large and in the Small: Theory and Experiment," Experimental Economics Center Working Paper Series 2008-01, Experimental Economics Center, Andrew Young School of Policy Studies, Georgia State University.
    5. Kaivanto, Kim, 2008. "Alternation Bias and the Parameterization of Cumulative Prospect Theory," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics, pages 91-107.
    6. Eike B. Kroll & Bodo Vogt, 2009. "The St. Petersburg Paradox despite risk-seeking preferences: An experimental study," FEMM Working Papers 09004, Otto-von-Guericke University Magdeburg, Faculty of Economics and Management.
    7. Szekely, Gabor J. & Richards, Donald S.t.P., 2004. "The St. Petersburg Paradox and the Crash of High-Tech Stocks in 2000," The American Statistician, American Statistical Association, vol. 58, pages 225-231, August.
    8. Samuelson, Paul A, 1977. "St. Petersburg Paradoxes: Defanged, Dissected, and Historically Described," Journal of Economic Literature, American Economic Association, vol. 15(1), pages 24-55, March.
    9. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
    10. Fishburn, Peter C, 1988. "Expected Utility: An Anniversary and a New Era," Journal of Risk and Uncertainty, Springer, vol. 1(3), pages 267-283, September.
    11. James C. Cox & Vjollca Sadiraj & Bodo Vogt & Utteeyo Dasgupta, 2007. "Is There A Plausible Theory for Risky Decisions?," Experimental Economics Center Working Paper Series 2007-05, Experimental Economics Center, Andrew Young School of Policy Studies, Georgia State University, revised Jun 2012.
    12. Aumann, Robert J., 1977. "The St. Petersburg paradox: A discussion of some recent comments," Journal of Economic Theory, Elsevier, vol. 14(2), pages 443-445, April.
    13. 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.
    14. Tibor Neugebauer & John Hey & Carmen Pasca, 2010. "Georges-Louis Leclerc de Buffon’s‘Essays on Moral Arithmetic’," LSF Research Working Paper Series 10-06, Luxembourg School of Finance, University of Luxembourg.
    15. Michael Birnbaum, 2005. "A Comparison of Five Models that Predict Violations of First-Order Stochastic Dominance in Risky Decision Making," Journal of Risk and Uncertainty, Springer, vol. 31(3), pages 263-287, December.
    16. David Durand, 1957. "Growth Stocks And The Petersburg Paradox," Journal of Finance, American Finance Association, vol. 12(3), pages 348-363, September.
    17. George J. Stigler, 1950. "The Development of Utility Theory. II," Journal of Political Economy, University of Chicago Press, vol. 58, pages 373-373.
    18. Mohammed Abdellaoui & John D. Hey (ed.), 2008. "Advances in Decision Making Under Risk and Uncertainty," Theory and Decision Library C, Springer, number 978-3-540-68437-4, July.
    19. James C. Cox & Vjollca Sadiraj & Bodo Vogt, 2009. "On the empirical relevance of st. petersburg lotteries," Economics Bulletin, AccessEcon, vol. 29(1), pages 214-220.
    20. William Vickrey, 1961. "Counterspeculation, Auctions, And Competitive Sealed Tenders," Journal of Finance, American Finance Association, vol. 16(1), pages 8-37, March.
    21. Szekely, Gabor J. & Richards, Donald S.t.P., 2005. "Response: Remain Steadfast With the St. Petersburg Paradox to Quantify Irrational Exuberance," The American Statistician, American Statistical Association, vol. 59, pages 235-239, August.
    22. Birnbaum, Michael H., 2004. "Tests of rank-dependent utility and cumulative prospect theory in gambles represented by natural frequencies: Effects of format, event framing, and branch splitting," Organizational Behavior and Human Decision Processes, Elsevier, vol. 95(1), pages 40-65, September.
    23. Rump, Christopher M., 2007. "Capital Growth and the St. Petersburg Game," The American Statistician, American Statistical Association, vol. 61, pages 213-217, August.
    24. Schmidt, Ulrich & Traub, Stefan, 2002. "An Experimental Test of Loss Aversion," Journal of Risk and Uncertainty, Springer, vol. 25(3), pages 233-249, November.
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    1. Ignoring Small Chances
      by Robin Hanson in Overcoming Bias on 2011-07-02 01:00:09

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    Cited by:

    1. Yukalov, V.I., 2021. "A resolution of St. Petersburg paradox," Journal of Mathematical Economics, Elsevier, vol. 97(C).
    2. Da Silva, Sergio & Matsushita, Raul, 2016. "The St. Petersburg paradox: An experimental solution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 445(C), pages 66-74.
    3. Tibor Neugebauer & John Hey & Carmen Pasca, 2010. "Georges-Louis Leclerc de Buffon’s‘Essays on Moral Arithmetic’," LSF Research Working Paper Series 10-06, Luxembourg School of Finance, University of Luxembourg.
    4. James C. Cox & Eike B. Kroll & Marcel Lichters & Vjollca Sadiraj & Bodo Vogt, 2019. "The St. Petersburg paradox despite risk-seeking preferences: an experimental study," Business Research, Springer;German Academic Association for Business Research, vol. 12(1), pages 27-44, April.
    5. Ruggero Paladini, 2017. "Il paradosso di S. Pietroburgo, una rassegna," Public Finance Research Papers 29, Istituto di Economia e Finanza, DSGE, Sapienza University of Rome.
    6. Daniel Muller & Tshilidzi Marwala, 2019. "Relative Net Utility and the Saint Petersburg Paradox," Papers 1910.09544, arXiv.org, revised May 2020.
    7. V. I. Yukalov, 2021. "A Resolution of St. Petersburg Paradox," Papers 2111.14635, arXiv.org.
    8. Riedl, A.M., 2012. "Experimental economics : economic and game theoretic principles in experimental research in the social sciences," Research Memorandum 001, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    9. Christian Seidl, 2013. "The St. Petersburg Paradox at 300," Journal of Risk and Uncertainty, Springer, vol. 46(3), pages 247-264, June.

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    More about this item

    Keywords

    Petersburg paradox; economic history; bounded rationality; significance level; experimental economics;
    All these keywords.

    JEL classification:

    • B3 - Schools of Economic Thought and Methodology - - History of Economic Thought: Individuals
    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • C9 - Mathematical and Quantitative Methods - - Design of Experiments
    • D8 - Microeconomics - - Information, Knowledge, and Uncertainty
    • G1 - Financial Economics - - General Financial Markets
    • N0 - Economic History - - General

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