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Keynes, Boole and the interval approach to probability

Author

Listed:
  • Michael Emmett Brady

    (California State University - Department of Operations Management)

  • Rogério Arthmar

    (Universidade Federal do Espírito Santo - Department of Economics)

Abstract

This paper provides evidence on how Keynes devised a mathematical framework for his system of probability, which he called «approximation», in A Treatise on Probability, 1921. Keynes used standard conditional, mathematical probability to duplicate Boole’s results in the Challenge problem. He also showed how Boole’s approach would lead to the specification of interval estimates. It is also demonstrated that Keynes provided a solid mathematical structure for his nonlinear, non-additive decision theory. We suggest he should be recognized as the founder of the modern nonadditive, nonlinear approach to probability.

Suggested Citation

  • Michael Emmett Brady & Rogério Arthmar, 2012. "Keynes, Boole and the interval approach to probability," History of Economic Ideas, Fabrizio Serra Editore, Pisa - Roma, vol. 20(3), pages 65-84.
    • Handle: RePEc:hid:journl:v:20:y:2012:3:6:p:65-84
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    Cited by:

    1. Richard Arena & Eric Nasica, 2021. "Keynes's Methodology and the Analysis of Economic Agent Behavior in a Complex World," GREDEG Working Papers 2021-10, Groupe de REcherche en Droit, Economie, Gestion (GREDEG CNRS), Université Côte d'Azur, France.
    2. Rog?rio Arthmar & Michael Emmett Brady, 2018. "Boole, Ramsey and the Keynes-Townshend exchanges on subjective probability," HISTORY OF ECONOMIC THOUGHT AND POLICY, FrancoAngeli Editore, vol. 2018(2), pages 55-74.
    3. Marcello Basili, 2013. "Ellsberg Rules and Keynes’s State of Long-Term Expectation: More Than an Accordance," Department of Economics University of Siena 685, Department of Economics, University of Siena.
    4. Marcello Basili & Carlo Zappia, 2018. "Ellsberg’s Decision Rules and Keynes’s Long-Term Expectations," Department of Economics University of Siena 777, Department of Economics, University of Siena.
    5. Carlo Zappia, 2021. "Keynes's Treatise on Probability at 100 Years: Its Most Enduring Message," GREDEG Working Papers 2021-36, Groupe de REcherche en Droit, Economie, Gestion (GREDEG CNRS), Université Côte d'Azur, France.
    6. Pedro Garcia Duarte, 2014. "Frank Ramsey," Working Papers, Department of Economics 2014_17, University of São Paulo (FEA-USP).

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