>From: Wei Dai <[EMAIL PROTECTED]>
>On Wed, Mar 21, 2001 at 09:39:10PM -0500, Jacques Mallah wrote:
> >     He thinks he is only 1/101 likely to be in round 1.  However, he 
>also knows that if he _is_ in round 1, the effect of his actions will be 
>magnified 100-fold.  Thus he will push button 2.
> >     You might see this better by thinking of measure as the # of copies 
>of him in operation.
> >     If he is in round 1, there is 1 copy operating.  The decision that 
>copy makes will affect the fate of all 100 copies of him.
> >     If he is in round 2, all 100 copies are running.  Thus any one copy 
>of him will effectively only decide its own fate and not that of its 99 
>brothers.
>
>You'll have to define what "effectively decide" means and how to apply that 
>concept generally. (Have you introduced it before? I think this is the 
>first time I've seen it.)

    I thought the meaning to be obvious in this context.  The simplest 
interpretation of your little experiment is that whatever fraction of him 
push a particular button, is the same fraction of him that end up with the 
corresponding payoff.  That's how I always interpreted it.
    If the measure of him is the same for the 2nd round as for after both 
rounds, then it's the same as if each copy gets to influence its own payoff.

>Suppose in round 2 he gets the $-9 payoff if any of the copies decide to 
>push button 1. Intuitvely, each copy affects the fate of every other copy.

    Now you're changing the game.  And it is a game, since as you said 
yourself, each guy affects the others.
    How will round 1 work?  Am I to assume that there is indeed just 1 copy 
active in round 1, or did you mean to say he gets -$9 if any fraction of him 
pushes 1 in round 1 as well?
    If not, and assuming there are 100 copies in round 2, he may be best 
advised to push 1 about 2% of the time, randomly chosen.  (I have not 
bothered to find the optimal solution for this game.)  That way, most of the 
time (98%) he will push 2 in round 1 and usually (~75%) still get the full 
payoff of pushing 1 in round 2.
    (On the other hand, if we assume an infinite # of copies and that round 
1 is also modified, then it is inevitable that at least some copies will get 
the idea to push 1 in both rounds.  So the thought processes of the majority 
of his copies is completely irrelevant, and the outcome is certain to be 
button 1 for both rounds.  Unless, that is, all copies are 100% identical 
with no access to a random # generator (Gieger counter, etc.); in that case, 
he will simply push button 2 as a matter of principle.)

> > >I suggest that he instead think
> > >"I'm in both round 1 and round 2, and I should give equal
> > >consideration to the effects of my decision in both rounds."
> >
> >     I assume you mean he should think "I am, or was, in round 1, and I 
>am, or will be, in round 2".  There is no need for him to think that, and 
>it's not true.  Only one of the "brothers" was in round 1.
>
>No, I meant he should think himself as being in both round 1 and round 2 
>"simultaneously", and making both decisions at once.

    I'm sorry to say it but that is ridiculous.  It makes no sense.  I hope 
you have not started to smoke the same weeds as the "1st person" crowd.

> >     First, anyone whose utility function does not depend on measure is 
>definately insane in my book.
> >     One good utility function could have the form
> > U = [sum_(thoughts) f(thought) M(thought)] + V
>
>I think anyone whose utility function does have that form is insane.

    Who isn't? :)  I admit it's not a perfect model, though.

>He's going to spend most of his resources running repeated simulations of 
>himself having the thought that he values most.

    Unlikely.  First, there may be no maximum of f.  For example, f could be 
proportional to the depth of the thought (roughly, the age the guy seems to 
be) as well as to a "happiness" factor.
    Second, it is unlikely that his resources would be such that doing so 
would maximize the utility.  Even if they are, it doesn't seem so strange 
that he would want to relive his happiest moment.

                         - - - - - - -
               Jacques Mallah ([EMAIL PROTECTED])
         Physicist  /  Many Worlder  /  Devil's Advocate
"I know what no one else knows" - 'Runaway Train', Soul Asylum
         My URL: http://hammer.prohosting.com/~mathmind/
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