The statement: "For example, Edwin T. Jaynes has published an argument [a reference here would be useful] based on Lie groups that if one is so uncertain about the value of the aforementioned proportion p that one knows only that at least one voter will vote for Kerry and at least one will not, then the conditional probability distribution of p given one's state of ignorance is the uniform distribution on the interval [0, 1]." seems highly improbable, unless Jaynes posthumously thought that the elctorate of the United States was infinite. --Henrygb 21:51, 19 Feb 2005 (UTC)

I think I know what's being referred to here. Jaynes wrote a paper, "Prior Probabilities," [IEEE Transactions of Systems Science and Cybernetics, SSC-4, Sept. 1968, 227-241], which I have reprinted in E. T. Jaynes: Papers on Probability, Statistics and Statistical Physics, Dordrecht, Holland: Reidel Publishing Company (1983), pp. 116-130. On p. 128 of my copy (corresponding to p. 239 of the IEEE paper, I presume) Jaynes, after deriving from a group-theoretic argument the prior θ ^{- 1}(1 - θ) ^{- 1}, remarks: "The prior (60) thus accounts for the kind of inductive inferences noted in the case of the chemical, which we all make intuitively. However, once we have seen at least one success and one failure, then we know that the experiment is a true binary one, in the sense of physical possibility, and from that point on all posterior distributions (69) remain normalized, permitting definite inferences about θ."

The reference to "the chemical" in this excerpt refers to Jaynes' example on the previous page, where he discusses a chemical dissolving or not dissolving in water, with the inference that it will do so reliably if it does so once; only when both cases are observed does one strongly think that the parameter might be on (0,1).

I infer from the passage that Jaynes would say that if we have one success and one failure, then for all other observations (excluding these two), the prior would be flat (after applying Bayes' theorem to these two observations using the prior displayed above).

Parenthetically, the Jeffreys prior, which many feel to be the right one in this case, is θ ^{- 1 / 2}(1 - θ) ^{- 1 / 2}--Billjefferys 18:50, 4 Apr 2005 (UTC)