Wei Dai writes:
> Now suppose that two people, Alice and Bob, somehow agree that a measure M
> is the objectively correct measure, but Bob insists on using measure M' in
> making decisions. He says "So what if universe A has a bigger measure than
> universe B according to M? I just care more about what happens in universe
> B than universe A, so I'll use M' which assigns a bigger measure to
> universe B." What can Alice say to Bob to convince him that he is
> not being rational? I don't see what the answer could be.

How about if she whacks him on the head?  Maybe that would knock some sense
into him.

Seriously, she could confront him with the reality that in the universe
branch they are in, measure M works, while M' does not.  Reality, whether
in the form of a knock on the head or more peaceful interactions, is
not subjective.

Now, true, there would be branches in the multiverse where M' worked
while M did not.  Believers in objective measure would say that those
branches are of low measure and so "don't matter", but as you point out,
Bob can argue symmetrically that this branch where he is stuck with
Alice and M has worked is also, to him, of low measure.

But we can solve this conundrum while retaining symmetry.  Rationality
should demand allegience to the observed measure.   It is irrational to
cling to a measure which has been rejected repeatedly by observations.
If classical definitions of rationality don't have this property, we
should fix them.  Bob is irrational to hold to M' in a universe whose
observations reveal M.

Now, this will demand that in White Rabbit universes, ones where the
quantum or thermodynamic laws just happen to fail due to bad luck, a
rational person would have to abandon his (correct!) belief in a lawful
universe and come to believe (incorrectly!) in miracles.  However this
is actually a reasonable requirement, since we are stipulating that such
miracles have been observed.

Hal Finney

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