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Fair Odds for Noisy Probabilities

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  • Ulrik W. Nash

Abstract

We suggest that one individual holds multiple degrees of belief about an outcome, given the evidence. We then investigate the implications of such noisy probabilities for a buyer and a seller of binary options and find the odds agreed upon to ensure zero-expectation betting, differ from those consistent with the relative frequency of outcomes. More precisely, the buyer and the seller agree to odds that are higher (lower) than the reciprocal of their averaged unbiased probabilities when this average indicates the outcome is more (less) likely to occur than chance. The favorite-longshot bias thereby emerges to establish the foundation of an equitable market. As corollaries, our work suggests the old-established way of revealing someone's degree of belief through wagers may be more problematic than previously thought, and implies that betting markets cannot generally promise to support rational decisions.

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  • Ulrik W. Nash, 2018. "Fair Odds for Noisy Probabilities," Papers 1811.12516, arXiv.org.
  • Handle: RePEc:arx:papers:1811.12516
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    References listed on IDEAS

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    1. Erik Snowberg & Justin Wolfers, 2010. "Explaining the Favorite-Long Shot Bias: Is it Risk-Love or Misperceptions?," Journal of Political Economy, University of Chicago Press, vol. 118(4), pages 723-746, August.
    2. Milton Friedman & L. J. Savage, 1952. "The Expected-Utility Hypothesis and the Measurability of Utility," Journal of Political Economy, University of Chicago Press, vol. 60(6), pages 463-463.
    3. Marco Ottaviani & Peter Norman Sorensen, 2010. "Noise, Information, and the Favorite-Longshot Bias in Parimutuel Predictions," American Economic Journal: Microeconomics, American Economic Association, vol. 2(1), pages 58-85, February.
    4. M. Andrea Pisauro & Elsa Fouragnan & Chris Retzler & Marios G. Philiastides, 2017. "Neural correlates of evidence accumulation during value-based decisions revealed via simultaneous EEG-fMRI," Nature Communications, Nature, vol. 8(1), pages 1-9, August.
    5. Ramsey, Frank P., 1926. "Truth and Probability," Histoy of Economic Thought Chapters, in: Braithwaite, R. B. (ed.),The Foundations of Mathematics and other Logical Essays, chapter 7, pages 156-198, McMaster University Archive for the History of Economic Thought.
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