Interesting Mathematical Paradox?

[jason1990]

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The indifference principle assumes that there is no effect.

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Is that correct?

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Let E be the event that we have the smaller envelope. Unconditioned, P(E) = 1/2. If we apply the indifference principle after looking at the value in the envelope, A, then we would conclude that P(E|A) = 1/2. Notice that this implies

P(A = x and E) = P(A = x)P(E | A = x) = P(A = x)P(E).

That is, under the indifference principle, A and E are independent. This is what I mean by "no effect."