Le 08-juil.-05, à 00:59, Lee Corbin a écrit :

Bruno writes

Each Lee-i is offered 5$ each time his bet is confirmed, but
loses 5$ if he makes a wrong bet.

And yes, it would be possible to emphasize to each instance that
he is to attempt to maximize "his own instance's" earnings.

Quite correct.

What will be your strategy in each version? Will your strategy differ?

Now if the Lees know all these facts, then they'll anticipate being
in both rooms upon each iteration. Therefore, they'll anticipate
losing $5 in one room and gaining $5 in the other. They'll also
realize that all bit sequences are being carried out. Therefore,
it doesn't make any difference whatsoever. The expectation of
each sequence is exactly the same number of dollars: zero.

I don't get the significance of this.

I don't understand your answer, and actually you did not answer. It
looks like you are forgetting I give you the choice between A, B, C, D.


You are asked to bet on your immediate and less immediate
future feeling. Precisely: we ask you to choose among the
following bets:

A. I will see 0 on the wall.
B. I will see 1 on the wall.
C. I will see 0 on the wall and I will see 1 on the wall.
D. I will see 0 on the wall or I will see 1 on the wall.

I choose C: insofar as I consider myself as a program, then
the program will see 0 on the wall and the program will also
see 1 on the wall. The program will experienced both. I will
experience both.

I guess you did choose C, without saying.


In that case you are correct the expectation will be zero. Are you sure
there is not a better strategy among A, B, C, D?

Why do you think that there is a better strategy?

C. will comport with all the facts.  And afterwards, when a poll
is conducted among all those who can prove that they are Lee Corbin
it will be found that half of them saw a 1 and half saw a zero.
It is preposterous to finger *any* of them and accuse them of
not being me.

They will each believe that they are me (i.e., the me here in the
past). That is, for each Lee', they will assert Lee' = Lee.
So also will Lee'' assert that Lee'' = Lee.  So IT'S FREAKING
OBVIOUS THAT Lee'' = Lee'.

Yet substitute someone else's name for mine in those equations,
and they'll demur.

As I said I have no problem with accepting Lee = Lee' = Lee'' (although I think this will entail Lee = Bruno at some point, but I have no problem with that and we can come back to this notion later). But I was not argumentating on personal identity, only on the problem you face when predicting your immediate future (or less future) experience. It is a different matter. I duplicate you iteratively, by annihilating (painlessly!) you and reconstituting you in the 0-room and the 1-room which differs from having a 0 (resp. 1) painted on a wall. And I let you choose between the bets A, B, C, D described above.

You choose C, that is: "I will see 0 on the wall and I will see 1 on the wall". Now, as I said this is ambiguous. So if I am in a bad mood, asking the first 0-Lee' about its immediate apprehension if he answers me "I am seeing 0 and I am seeing 1" I consider it as false (0-Lee' sees only 0!), and the same for the other Lee, so all the 2^n Lee must give 5$. If I am in a good mood, I accept your reasoning and you loose nothing, but also you win nothing.

Why not choosing D, that is "I will see 0 on the wall OR I will see 1 on the wall." I recall you that "p or q" is true if p is true or q is true. So with D all the Lee will win. D consists into admitting that you are ignorant about your immediate apprehension after the duplication. It has nothing to do with the fact that you are the two Lee.




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