Analysis Advance Access published online on September 28, 2009
Analysis, doi:10.1093/analys/anp124
© The Author 2009. Published by Oxford University Press on behalf of The Analysis Trust. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org
On Bertrand's paradox
University of Cambridge HPS Cambridge, UK sib24@cam.ac.uk
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The Principle of Indifference1 (PI) instructs us that in the absence of background information equal portions of the possibility space should be assigned equal probabilities.2 PI is a central element of the ‘classical’ conception of probability, but, for all its strong intuitive appeal, it is widely believed that it faces a devastating objection: the so-called (by Poincaré) ‘Bertrand paradoxes’ (in essence, cases in which the same probability question receives different answers). The puzzle has fascinated many since its discovery, and a series of clever solutions (followed promptly by equally clever rebuttals) have been proposed.3 However, despite the long-standing interest in this problem, an important assumption, necessary for its generation, has been overlooked. My aim in this note is to identify this assumption. Since what it claims turns out to be prima facie problematic, I will urge that the burden of proof now shifts to the objectors to PI; they have