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From: Hal Finney <hal.domain.name.hidden>

Date: Fri, 10 Jan 2003 17:21:13 -0800

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.

Hal Finney

Received on Fri Jan 10 2003 - 20:23:14 PST

Date: Fri, 10 Jan 2003 17:21:13 -0800

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.

Hal Finney

Received on Fri Jan 10 2003 - 20:23:14 PST

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