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Far from the Madding Crowd: Collective Wisdom in Prediction Markets

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  • Giulio Bottazzi
  • Daniele Giachini

Abstract

We investigate market selection and bet pricing in a simple Arrow security economy which we show is equivalent to the repeated prediction mar- ket models studied in the literature. We derive the condition for long run survival of more than one agent (the crowd) and quantify the information content of prevailing prices in the case of two fractional Kelly traders with heterogeneous beliefs. It turns out that, apart some non-generic situations, prices do not converge, neither almost surely nor on average, to true probabilities. Nor are they always nearer to the truth than the believes of all surviving agents. Moreover, we show that by adapting their beliefs to past prices, agents further decrease the agreement between market prices and true probabilities.

Suggested Citation

  • Giulio Bottazzi & Daniele Giachini, 2016. "Far from the Madding Crowd: Collective Wisdom in Prediction Markets," LEM Papers Series 2016/14, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
  • Handle: RePEc:ssa:lemwps:2016/14
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    References listed on IDEAS

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    1. Manski, Charles F., 2006. "Interpreting the predictions of prediction markets," Economics Letters, Elsevier, vol. 91(3), pages 425-429, June.
    2. He, Xue-Zhong & Treich, Nicolas, 2012. "Heterogeneous Beliefs and Prediction Market Accuracy," IDEI Working Papers 775, Institut d'Économie Industrielle (IDEI), Toulouse.
    3. L. C. MacLean & W. T. Ziemba & G. Blazenko, 1992. "Growth Versus Security in Dynamic Investment Analysis," Management Science, INFORMS, vol. 38(11), pages 1562-1585, November.
    4. Bottazzi, Giulio & Dindo, Pietro, 2014. "Evolution and market behavior with endogenous investment rules," Journal of Economic Dynamics and Control, Elsevier, vol. 48(C), pages 121-146.
    5. Charles A. Holt & Susan K. Laury, 2002. "Risk Aversion and Incentive Effects," American Economic Review, American Economic Association, vol. 92(5), pages 1644-1655, December.
    6. Giulio Bottazzi & Pietro Dindo, 2013. "Selection in asset markets: the good, the bad, and the unknown," Journal of Evolutionary Economics, Springer, vol. 23(3), pages 641-661, July.
    7. Wolfers, Justin & Zitzewitz, Eric, 2006. "Interpreting Prediction Market Prices as Probabilities," IZA Discussion Papers 2092, Institute for the Study of Labor (IZA).
    8. Giulio Bottazzi & Pietro Dindo, 2015. "Drift criteria for persistence of discrete stochastic processes on the line," LEM Papers Series 2015/26, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
    9. Leonard Maclean & William Ziemba & Yuming Li, 2005. "Time to wealth goals in capital accumulation," Quantitative Finance, Taylor & Francis Journals, vol. 5(4), pages 343-355.
    10. MacLean, Leonard C. & Sanegre, Rafael & Zhao, Yonggan & Ziemba, William T., 2004. "Capital growth with security," Journal of Economic Dynamics and Control, Elsevier, vol. 28(5), pages 937-954, February.
    11. repec:reg:rpubli:460 is not listed on IDEAS
    12. Blume, Lawrence & Easley, David, 1992. "Evolution and market behavior," Journal of Economic Theory, Elsevier, vol. 58(1), pages 9-40, October.
    13. Leonard MacLean & William Ziemba, 1999. "Growth versus security tradeoffs indynamic investment analysis," Annals of Operations Research, Springer, vol. 85(0), pages 193-225, January.
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    Cited by:

    1. Bottazzi, Giulio & Giachini, Daniele, 2017. "Wealth and price distribution by diffusive approximation in a repeated prediction market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 473-479.

    More about this item

    Keywords

    Prediction Markets; Bet Pricing; Wisdom of Crowds; Market Selection; Heterogeneous Beliefs; Fractional Kelly Rule;

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