With regard to the question of the significance or impact of the MWI,
this is where Wei Dai's emphasis on the importance of decision theory
comes in. The question is, are there things we would rationally do
differently if we knew that all possible worlds existed, things that
would be irrational in a single universe?
In a single-world model we have uncertainty about the world we live in,
its past, present and future. This can be captured by a probability
distribution over possible worlds. We then use that probability
distribution to make our decisions. But in a many-worlds model, we
also have a probability distribution over possible worlds, and we would
also use that probability distribution to make decisions. Given this
similarity, are there cases where we would rationally decide differently
in the many-worlds universe than in the single-world universe?
Wei explored some possibilities along these lines in his postings
in mid 2002. One such situation could be demonstrated with a simple
thought experiment. Suppose you are going to flip a coin, and you will
be given a piece of fruit as a result, either an apple or an orange.
Also suppose that beforehand you can decide which kind of fruit you will
be given for each of the two possible coin flip outcomes: for example,
you could receive an orange on heads and an apple on tails, or any of
the other three possibilities. Let us also suppose that you like both
fruits but slightly prefer apples to oranges.
Conventional decision theory is designed to handle exactly this sort
of situation. According to those principles, you would act to maximize
your expected utility. Since you get more utility from an apple than
from an orange, and the coin flip has a 50-50 chance of coming up
heads or tails, your expected utility is maximized by specifying that
you will get an apple whether the coin falls heads or tails. This is
very obvious even without being expressed in the mathematical form that
decision theory uses.
Wei suggested that in the context of a many-worlds universe (not just
the quantum MWI but even for a broader set of possibilities), you might
not make this same decision. You know that when the coin flips, the
universe is going to effectively branch and both possibilities are going
to be actualized. Let us suppose that in addition to slightly preferring
apples to oranges, you have a strong value preference for diversity.
You like variety and you dislike having everything the same everywhere.
In that case, you might rationally choose to receive an apple on heads
but an orange on tails. While this slightly reduces your average
pleasure level in terms of tasting the fruit, this could be more than
compensated by your increased pleasure at knowing that you are enjoying
diverse experiences in the two worlds.
So here is an example where belief in multiple worlds could lead a
rational person to behave differently than belief in a single world.
For this effect to occur, I think our preferences in the many-worlds
case have to depend on relations between the worlds, rather than
independently on conditions in each world. We're not just acting to
maximize the expected outcome in each world averaged across all of them,
we're acting to maximize the utility of the "big picture", the entire
set of worlds affected by our acts, considered as a whole. To the extent
that a whole is more than the sum of its parts, actions in a multiverse
model may justifiably be different than in a single universe.