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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)
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*> that in every case, the utility of getting both payoffs is x1+x2 where
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*> the individual payoffs are worth x1 and x2. This would seem to correspond
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*> to your shoe example, where getting a left + right shoe is worth much
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*> more than getting just a left or just a right shoe.
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*>
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*> Rather, he is saying that for those cases where the payoffs are additive,
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*> 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

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 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

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