On 20-Mar-01, Wei Dai wrote:
> Suppose the new experiment has two rounds. In each round the
> participant will be given temporary amnesia so he can't tell which
> round he is in. In round one he will have low measure (1/100 of
> normal). In round two he will have normal measure. He is also told:
> If you push button 1, you will lose $9.
> If you push button 2 and you are in round 1, you will win $10.
> If you push button 2 and you are in round 2, you will lose $10.
> According to anthropic reasoning, the participant when faced with the
> choices should think that he is much more likely to be in round 2, and
> therefore push button 1 in both rounds, but obviously he would have
> been better off pushing button 2 in both rounds.
I don't see any paradox. This is no different than:
If you push button 1, you will lose $9.
If you push button 2 you will win $10 one time out of 101 at random.
The other 100 times out of 101 you will lose $10.
If you push 1 your expected payoff is -$9.
If you push 2 your expected payoff is ($10*1 - $10*100)/101=-$9/1.01
So you push 2. Where's the paradox?