Dear Wei, Two ideas would seem to mute this strange thought.
1) The no-cloning theorem, iff the world follows QM and not just classical physics. 2) van Fraassen's Reflection Principle seems to ignore the possibility that probabilities and their distributions are given ab inition and that the notion of "updating" and/or revising one's expectations is negligible. Kindest regards, Stephen ----- Original Message ----- From: "Wei Dai" <[EMAIL PROTECTED]> To: "Marchal Bruno" <[EMAIL PROTECTED]> Cc: <[EMAIL PROTECTED]> Sent: Wednesday, December 18, 2002 8:15 PM Subject: Re: Quantum Probability and Decision Theory > 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. > >