, Volume 186, Issue 2, pp 447–474

Bayesian chance


DOI: 10.1007/s11229-011-9994-5

Cite this article as:
Harper, W., Chow, S.J. & Murray, G. Synthese (2012) 186: 447. doi:10.1007/s11229-011-9994-5


This paper explores how the Bayesian program benefits from allowing for objective chance as well as subjective degree of belief. It applies David Lewis’s Principal Principle and David Christensen’s principle of informed preference to defend Howard Raiffa’s appeal to preferences between reference lotteries and scaling lotteries to represent degrees of belief. It goes on to outline the role of objective lotteries in an application of rationality axioms equivalent to the existence of a utility assignment to represent preferences in Savage’s famous omelet example of a rational choice problem. An example motivating causal decision theory illustrates the need for representing subjunctive dependencies to do justice to intuitive examples where epistemic and causal independence come apart. We argue to extend Lewis’s account of chance as a guide to epistemic probability to include De Finetti’s convergence results. We explore Diachronic Dutch book arguments as illustrating commitments for treating transitions as learning experiences. Finally, we explore implications for Martingale convergence results for motivating commitment to objective chances.


Objective chanceSubjective degree of beliefReference lotteriesUtility axiomsDutch booksMartingale convergence

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  • William Harper
    • 1
  • Sheldon J. Chow
    • 1
  • Gemma Murray
    • 1
  1. 1.The University of Western OntarioLondonCanada