GSLevy wrote:
>I agree that the implicit distribution of m is essential in determining if
>we
>should switch after making our first choice. Interestingly, if we assume a
>logarithmic distribution and compute the expected value of the content of
>the
>other box (the one not selected), we find that it is identical to the
>content
>of the selected box:
>
>Expected Value = (1/2) (Log(m/2) + Log(2m)) = (1/2) (Log(m) - Log2 + Log(m)
>+ Log2)
> = Log(m)
>
>Which implies that the logarithmic distribution is the one assumed by common
>sense: don't switch. In other words, the value that any particular number is
>equal to m is equally likely, and INDEPENDENT OF SCALE. This independence of
>scale has some intriguing connection with the MWI and the issue that the
>probability of survival after death is extremely low but FROM THE POINT OF
>VIEW of the observer it must be equal to one.
It seems to me that this remark is very interesting.
I would nevertheless be very
pleased if you could give some more precise hints about the
connection between the mentionned independance of scale and MWI (and the
*immortality* issue).
Bruno.
Bruno MARCHAL Phone : +32 (0)2 6502711
Universite Libre Fax : +32 (0)2 6502715
de Bruxelles Prive : +32 (0)2 3439666
Avenue F.D. Roosevelt, 50 IRIDIA, CP 194/6
B-1050 BRUSSELS Email : marchal.domain.name.hidden
Belgium URL :
http://iridia.ulb.ac.be/~marchal
Received on Tue May 11 1999 - 00:31:50 PDT