Re: Quantum Probability and Decision Theory

From: Wei Dai <weidai.domain.name.hidden>
Date: Wed, 18 Dec 2002 20:15:27 -0500

On Wed, Dec 04, 2002 at 04:00:07PM +0100, Marchal Bruno wrote:
> Have you read the "revisited" paper by Wallace on Everett/decision
> theory? Quite interesting imo, and relevant for some discussion,
> about MWI and decision theory we have had on this list.
>
> http://philsci-archive.pitt.edu/documents/disk0/00/00/08/85/index.html

Thanks for this pointer. I highly recommend this paper as well, for an
introduction to decision theory and an example its implications.
Unfortunately the author is not aware of some serious problems with the
subjective-indeterministic version of decision theory that he adopts,
which we've discussed on this list in the past. I'll attach an email that
I sent him summarizing the problems with the subjective-indeterministic
view.

---
1. The SI viewpoint is not evolutionarily adaptive if copying is possible. 
Suppose a company invents a non-destructive matter-transporter and offers 
to create copies of paying customers on distant planets with the 
opportunity to colonize them. And suppose the expected living standards on 
the colonized planets would be just slightly lower than those on Earth. 
Those who accept the SI viewpoint would refuse to pay anything for this 
service, since it would lower their expected utility. The universe would
quickly be dominated by the OD viewpoint.
2. A similar issue arises in quantum splitting. In a thought experiment 
that Max Tegmark calls quantum suicide (see his "The Interpretation of 
Quantum Mechanics: Many Worlds or Many Words?" available at 
http://www.hep.upenn.edu/~max/everett.html), the experimenter is killed 
every time a quantum measurement comes out a certain way (say spin up). 
People who accept the SI viewpoint will have no problem with doing this 
experiment. People who accept OD can actually benefit at their expense, 
for example by offering to gamble with the experimenter on the outcome of 
the measurement. The experimenter will believe that the probability of 
spin down is 1, and will accept any odds on a gamble that pays on spin 
down.
3. The SI viewpoint either contradicts van Fraassen's Reflection Principle 
or leads to counterintuitive results. Saunders tries to address this in 
his paper (section 4.3) but I don't think his argument is convincing. 
Consider Fig.1 in his paper (page 15, at 
http://philsci-archive.pitt.edu/documents/disk0/00/00/04/65/ in case you 
don't have it handy). Before the copying, it seems reasonable to follow 
Saunders and assign 1/4, 1/4, and 1/2 to the probabilities of E, E', and 
E'' respectively. But consider after copying, when you're one of the three 
copies of A1 but don't know which one yet. I think anyone who has worked 
with computers will say that all exact copies are equivalent, and the 
"history" of how the copies are done is irrelevent. Thus there is a strong 
intuition that after copying, the probabilities should be 1/3, 1/3, 1/3.
4. Something similar to 3 happens with quantum suicide. Suppose you do two 
independent spin measurements, creating four branches, and label them 
(0,0),(0,1),(1,0),(1,1) according to the results of the measurements. And 
suppose you set up your quantum suicide machine to tell you the result of 
the first measurement, kill you if you're in branch (0,0) and then tell 
you the result of the second measurement. Before the experiment begins, it 
seems reasonable to believe that the probabilities of ending up in 
(0,1),(1,0),(1,1) are 1/2, 1/4, and 1/4, but afterwards it seems they 
should be 1/3, 1/3, and 1/3. (BTW, what is the answer according to the QS 
axioms?)
5. The SI perspective does not allow preferences for diversity of
experience across branches or copies. (This is what I brought up in my
earlier email.) In the case of copying, this is again an evolutionary
disadvantage.
So I think the SI perspective is seriously flawed, but as you point out 
the OD perspective also has its problems. Adopting OD would require 
abandoning our current concept of probability and everything based on it, 
which of course no one wants to do. At this point I'm not sure what the 
answer is. One answer may be that the QS axioms can be thought of as 
approximately describing the preferences of most people, except for their 
preferences about copying and quantum suicide, and so they can use 
probabilities as a tool for making decisions but with the understanding 
that it's only an instrument with limited accuracy and application.

Received on Wed Dec 18 2002 - 20:16:48 PST