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From: jillbones on 9 Oct 2009 17:52
On Oct 1, 11:13 am, Len <lwapn...(a)gmail.com> wrote:
> Can someone offer a resolution?
>
> The content of each of two identical envelopes is determined by a
> “St. Petersburg procedure”.  A fair coin is tossed repeatedly until
> heads first appears.  If heads appears on the first toss, $2 will be
> placed in one envelope.  If heads does not appear until the second
> toss, $4 will be placed in that envelope.  If three tosses are
> required, $8 goes into the envelope, and so on, doubling the amount
> for each additional required toss of the coin.  So, in general, if n
> tosses are required, $2^n goes into the envelope.  The envelope is
> sealed and the expected value of the content is infinite.  That is,
> one should be willing to pay any finite amount of money in exchange
> for the unknown content of the envelope.  (I wish to ignore utility
> considerations.  Or, simply assume the contents are utils, as opposed
> to dollars.)   A similar procedure is independently employed to fill
> the second envelope.  It too is sealed.
>
> You randomly select an envelope and observe its content.  You may keep
> the content or exchange it for the other, unopened envelope.  Should
> you be willing to do so?
>
> One could argue “yes”, by the above discussion.  But if this were the
> case, one should always be willing to make the exchange.  Why open the
> selected envelope?  Just switch!  By symmetry this seems ludicrous.
>
> Resolution?
>
> Thanks,
>
> Len

Before it is opened, the selected envelope also has an theoretical EV
of infinity. Therefore, there is no
reason to arbitrarily reject the selected envelope,
before ascertaining its contents.





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