> Suppose there are only two logically possible deterministic universes A
> and B, and you know that A has measure 0.9, and B has measure 0.1. Suppose
> that until time T the history of these two universes are identical. At
> time T an experiment will be done in both universes. In universe A the
> outcome of the experiment will be "a", and in universe B the outcome will
> be "b". If before time T you were given an opportunity to bet $10 that the
> outcome is "a" at 1:1 odds, so that in universe A you would gain $10, and
> in universe B you would lose $10, Would you take the bet?
Measure is not supposed to be just an abstract number that is attached
to a universe. It has meaning in terms of our own perceptions and
experience in that universe. The all-universe theory includes both a
model of universes which exist, and a way of relating our experiences of
consciousness to those universes. In the theory, if there is a physical
system in the multiverse which is isomorphic to our own mental state, then
the probability of experiencing subjective consequences which correspond
to changes in that system will be proportional to its measure. This is
a crucial linkage for the theory to have explanatory power, otherwise
our experiences would not need to have any connection to measure and it
would be a meaningless parameter.
> The standard answer is yes, you should take it because A has greater
> measure. But that assumes you care more about universes that have greater
> measure than universes that have less measure. But you could say that you
> don't care about what happens in universe A, only about what happens in
> universe B, in which case you wouldn't take the bet. So it seems that the
> measure only affects your decisions if it enters into your utility
> function somehow, and it's not clear that it must.
Think of a single-universe model with ordinary probability, where you
have a bet with a 90% chance of outcome A and 10% chance of outcome B.
Conventionally you should take the bet which maximizes your expectations
based on A occuring. But you could imagine someone who only cared about
what happened if outcome B happened, and bet on B so that he would do
well in that unlikely case. It's rational in a certain sense, but it
is going to lead to bad consequences in practice.
These two examples are similar in that in each case you have to face the
reality that you are likely to subjectively experience outcome A. In the
multiverse model that is part of the theory which relates subjective
experience to the physical model. You can't escape the fact that the
subjective consequences of your actions will be based on measure. So
I don't think you can ignore it or treat it as a parameter to be dealt
with as you like.