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
Received on Tue Jan 14 2003 - 14:24:24 PST
This archive was generated by hypermail 2.3.0
: Fri Feb 16 2018 - 13:20:08 PST