Re: David Deutsch on probability in the MWI

From: Wei Dai <weidai.domain.name.hidden>
Date: Tue, 8 Jun 1999 14:45:26 -0700

On Mon, Jun 07, 1999 at 06:55:29PM -0700, hal.domain.name.hidden wrote:
> 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.

I don't think that is what is saying. In classical probability based
decision theory, utility functions are assumed to satisfy the condition
that U(Z) = (U(X)+U(Y))/2, where Z is a 50/50 lottery ticket for getting
either X or Y. This is needed in order to obtain a unique utility function
for each possible set of preferences (technically it's only unique up to a
linear transformation), and for the "maximize expected utility" idea work.

Deutsch apparently wants to derive this condition from his additivity
condition. That condition says U(Z') = U(X)+U(Y), where Z' is getting both
X and Y. But, the preferences of most real people CANNOT be described by a
utility function that satisfies additivity (see my shoe example). So what
Deutsch has really shown is that an utility function U that satisfies
additivity must also satisfy U(Z) = (U(X)+U(Y))/2, where Z is a 50/50
quantum lottery tick for getting either X or Y. But the result is
meaningless since people's preferences cannot be described by this kind of
utility functions.
Received on Tue Jun 08 1999 - 14:46:47 PDT