Answering the last question first, "Do you find this perspective useful?"...

I'm not yet convinced of any of the utility of the MWI for any bet or action, but I certainly think you are pursuing something that _might_ be interesting or even useful, with a kind of "quantum decision theory" view. But I've yet to see anything convincing.

More comments:

On Monday, January 13, 2003, at 02:33 PM, Wei Dai wrote:

On Fri, Jan 10, 2003 at 08:54:38PM -0800, Tim May wrote:
But in this, the only universe I will ever, ever have contact with, I
optimize as best I can. And I assume all the myriad mes are doing the
same in their universes, forever disconnected from mine.
You're taking the question too personally. The issue here is whether
rationality only involves local optimization within the branch that one is
in without regard to other branches, or whether one can also take into
account what one believes to be happening in other branches. You yourself
may be a local optimizer, but the larger question is whether rationality
allows global optimization or not. Notice that the latter is more
general than the former, because all local optimizers can be modeled as
global optimizers with a special form of utility function.
I would like to see some better examples of what these "take into account what one believes to be happening in other branches" decisions or optimizations might be.

If in fact the branches are unreachable to us, then causally there can be no effect of one branch on another. From the causal decision theory I believe you support (Joyce's book), this is just about a perfect example of where causal decision theory says "no causal link."

Now, as I discussed in reply to Hal, there's much evidence that what people _believe_ affects their actions in this world, this branch. But this is true without recourse to many worlds theories. A person's belief in an afterlife usually affects his actions in this life. Examples abound, and were we talking or arguing in the room I described in my first post today, we might consider a bunch of them.

R.I.G. Hughes, in "The Structure and Interpretation of Quantum Mechanics," 1989, discusses this issue of betting in a MWI environment:

(late in the book, after much discussion of operators, lattices propositions, measurements, interpretations, probability measures, etc.)

"But what, on Everett's account, has become of the world which is actual in Lewis's? If there is no such privileged world, then something odd happens to our conception of probability. For if _all_ (relevant) events with nonzero probability are realized in some world or other, then are not all those events certain of occurrence? (This was pointed out by Healey, 1984, p 593.) And if I wager on what the outcome of a measurement will be, will it not pay "me" to place my bet on whatever outcome is quoted at the highest odds, without regard to the probabilities involved? ...... (Before an epidemic of long-odds betting is upon us, however, I should add that even the National Security Council would be hard put to divert funds from my Swiss bank account in one world to its counterpart in another.)

"These levities aside, we may ask what new understanding of the measurement process MWI gives us. After a measurement each observer will inhabit a world (for her the actual world) in which a particular result of the measurement has occurred. And the "total lack of effect of one branch on another also implies that no observer will ever be aware of any 'splitting' process" (Everett, 1947, p. 147n). What is this observer to say about the physical process which has just occurred? From where she stands, the wave packet has collapsed no less mysteriously , albeit no more so, than before."

"We are still left with the dualism that the interpretation sought to eradicate. As de Witt (1970, pp. 164-165) himself remarks, the many-worlds interpretation of quantum mechanics "leads to experimental predictions identical with the (dualist) Copenhagen view.""

(p. 293)

(Tim again.) Now we all know this, but it makes the point that probabilities are calculated identically in both interpretations.

If Wei can find a way, no pun intended, to show that "quantum decision theory" produces different results OTHER THAN THOSE BASED ONLY ON THE BELIEF ITSELF, this would seem to contradict the "identical experimental predictions" and would be an important contribution.

(Excluding results based only on the "BELIEF ITSELF" means that it is not kosher or persuasive to argue that because someone's belief changes their actions it must mean that the belief is correct. If this were allowed, Allah's suicide bombers would be proof that Islam is right, and so on, for every religious and other belief.)

My point is that since there doesn't seem to be a reason to disallow
global optimization, it shouldn't be ruled out. I'm interested in
a decision theory that allows global optimization and want to know its
practical and philosophical consequences.
I would rule it out in terms of causal decision theory by the very fact that the standard model (of MWI) posits no causal flow amongst branches. So, by the most basic sort of CDT, how could actions in one branch affect things in other branches?

As Joyce puts it, initially quoting Allan Gibbard and William Harper,

" "The "utility" of an act should be its expected efficacy in bringing about states of affairs the agent wants, not the degree to which news of the act ought to cheer the agent...."

"The point here is that rational decision makers should choose actions on the basis of their _efficacy in bringing out desirable results_ rather than their auspiciousness as harbingers of these results."

(p. 150, "The Foundations of Causal Decision Theory," 1999.)

Now in Hal's retelling of your model, Alice occasionally chooses non-optimal choices of rewards in a game of chance precisely because she hopes that other Alices in other worlds will do the same and that this will increase diversity in the Multiverse. But how can such behavior in other worlds affect _her_ world, the world where she made a sub-optimal choice? Isn't this the "good news" fallacy writ large?

(By the way, there is an interpretation under which Alice sometimes does "the unexpected" because it adds to her own joy in her own universe. One might say that "sometimes picking a non-optimal result makes here a more interesting person." But this is all done with conventional single-track notions of probability, of "karma" (in the personality sense, not in a religious sense), etc. Sometimes doing the unexpected also may enhance her survival (landscape exploration) or problem-solving, by having new experiences of vantage points. Google has an "I'm feeling lucky" button on its search pane, and casting I Ching or Tarot cards may have the "thinking outside the box" effects for some. All of these actually involve "meta-optimizing" Alice even by locally choosing non-optimal results sometimes. An appeal to Alice' and Alice'', etc., in other branches is neither useful nor helpful, as I see things.)

If you guys can think of some better examples, I'll be very interested.

On the question of QS, I think all QS'ers can also be modeled as global
optimizers with a special form of utility function. From this perspective,
the disagreement between QS'ers and local optimizers like Tim can be seen
as a difference of opinion on what kind of utility function one should
have. (Personally I'm not convinced by either side and I'm not sure how to
answer the question myself.) Do you find this perspective useful?
As I said, I think your quest is potentially useful. If you come up with actual predictions which differ from normal predictions--modulo the point that they are not based on Alice's "belief" qua belief--then you will have perhaps _experimentally_ distinguished MWI from other interpretations, something no one has been able to do so far.

But such an extraordinary result will require much debate before many of us are persuaded.

Good luck! (Imagine, in a large number of universes you have already found such a proof...the challenge is getting it to those of us in this our only universe.)

--Tim May
(.sig for Everything list background)
Corralitos, CA. Born in 1951. Retired from Intel in 1986.
Current main interest: category and topos theory, math, quantum reality, cosmology.
Background: physics, Intel, crypto, Cypherpunks

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