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By Hideo Kusuoka and Julien I.E. Hoffman

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Laplace 1952, p. 6] If [the various cases] are not [equally possible], we will determine first their respective possibilities, whose exact appreciation is one of the most delicate points of the theory of chance. [Laplace 1952, p. 11] To assign equal probability to cases “such as we may be equally undecided about” is the notorious principle of insufficient reason. Although Laplace did not view it as controversial, many in the nineteenth century did. What determines when cases are equally probable, possible, or likely?

New York: Dover, 1953), pp. 133– 134. In Kraitchik’s version two persons compare their neckties, the person with the less valuable necktie to receive both. 29. I thank Persi Diaconis, David Malament, and Brian Skyrms for helpful comments. 33 REFERENCES Arbuthnot, John (1711). ‘An argument for divine providence taken from the constant regularity observed in the births of both sexes’, Philosophical Transactions of the Royal Society of London 27, 186–190. Baker, Keith Michael (1975). Condorcet: From Natural Philosophy to Social Mathematics (Chicago: University of Chicago Press).

Donkin’s paper, although little known, is a lucid and careful attempt to clarify the foundations of the subject. It was written in response to criticisms by Forbes and others of Michell’s argument that stars that are optically double are also physically so. Donkin begins by stating that It will, I suppose, be generally admitted, and has often been more or less explicitly stated, that the subject matter of calculation in the mathematical theory of probabilities is quantity of belief. 18 Donkin’s philosophical view of probability may be summarized as relative, logical, numerical, and consistent.

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