Re: David Deutsch on probability in the MWI

From: <hal.domain.name.hidden>
Date: Mon, 7 Jun 1999 18:55:29 -0700

Wei Dai, <weidai.domain.name.hidden>, writes:
> "And let us consider only players for whom the
> utilities of the possible payoffs can be assigned so as to have an
> additivity property, namely that the player is indifferent between
> receiving two separate payoffs with utilities x1 and x2, and receiving a
> single payoff with utility x1+x2."
> [...]
> BTW it's easy to see why these people don't exist. Additivity implies that
> you either prefer two left shoes to a matched pair, or you prefer two right
> shoes to a matched pair, or you are indifferent between all three choices.

I think that the assumption David Deutsch intends may be different from
what you are reading. He is not saying (as I think you are reading him)
that in every case, the utility of getting both payoffs is x1+x2 where
the individual payoffs are worth x1 and x2. This would seem to correspond
to your shoe example, where getting a left + right shoe is worth much
more than getting just a left or just a right shoe.

Rather, he is saying that for those cases where the payoffs are additive,
you don't care whether you get them both at once or one at a time.

The first place he uses this assumption is:

"This is proved by appealing twice to the additivity of utilities. First,
receiving any of the possible payoffs xa + k of the game referred to on
the left of (8) has, by additivity, the same utility as receiving the
payoff xa followed by the payoff k."

He is saying that the player is indifferent between getting a payoff
with utility xa+k and getting one worth xa followed by one worth k.

Hal
Received on Mon Jun 07 1999 - 18:59:29 PDT