Consider the following thought experiment. 

Two volunteers who don't know each other, Alice and Bob, are given
temporary amnesia and placed in identical virtual environments. They are
then both presented with three buttons and told the following:

If you push 1, you will lose $9
If you push 2 and you are Alice, you will win $10
If you push 2 and you are Bob, you will lose $10

I'll assume that everyone agrees that both people will push button 2.

The paradox is what happens if we run Alice and Bob's minds on different
substrates, so that Bob's mind has a much higher measure than Alice's. If
they apply anthropic reasoning they'll both think they're much more likely
to be Bob than Alice, and push button 1.

If you don't think this is paradoxical, suppose we repeat the choice but
with the payoffs for button 2 reversed, so that Bob wins $10 instead of
Alice, and we also swap the two minds so that Alice is running on the
substrate that generates more measure instead of Bob. They'll again both
push button 1. But notice that at the end both people would have been
better off if they pushed button 2 in both rounds.

Any anthropic reasoning proponents want to tackle this?

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