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RichardKennaway comments on The Bias You Didn't Expect - Less Wrong
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You've lost me completely.
If we're talking about the probabilities of X and Y, as you say here, then the evidence against them lowers those probabilities, and the fact that the debate in your abstract example is over whether X or Y is correct doesn't change that. It is a situation where both are less likely than they were before C was known.
If your basic point is consistent with that, then I do not understand your basic point. It sure sounds to me like your basic point was that C made one of those assertions more likely, which is false.
I believe brazil84 is describing this:
P(X | C & (X v Y)) > P(X | X v Y)
P(Y | C & (X v Y)) < P(Y | X v Y)
while you are describing this:
P(X | C) < P(X)
P(Y | C) < P(Y)
All four of these statements can be true.
(nods)
See also alejandro1's sibling comment and my reply.