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thomblake comments on Conditioning on Observers - Less Wrong
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Suppose two weeks' worth of coins are tossed ahead of time.
Then with probability 1/4, you will wake up twice in the evening. With probability 1/2, you will wake up 6 times in the morning and once in the evening. And with probability 1/4 you will wake up 12 times in the morning.
Then by your logic, you ought to say that your probability of waking in the morning is (1/4)x(0/2) + (1/2)x(6/7) + (1/4)x(12/12) = 3/7 + 1/4 = 19/28, rather than 1/2 if the coins are tossed 'just in time'.
How can whether the coins are tossed in advance or not change the subjective probability?
By neq1's previous reasoning, there's 50% chance of waking in the mornings and 50% chance of waking in the evening for any particular week. That is the case whether the coins are tossed in advance or not. The probability of a particular morning awakening would be 1/12.
I'm not sure where you got your (6/7) figure for neq1's calculations.
neq1 admits that in my original scenario, before I introduced the coin and hibernations, you have a 6/7 probability of waking in the morning. The case where one of the two coins is heads and the other is tails is equivalent to this.