[I am starting a new thread on this question because I feel I may have
confused matters with increasingly elaborate thought experiments in my posts
to Eric Cavalcanti's thread on observation selection effects.]
The occurence of events which at first glance seem to be very unlikely
should not necessarily surprise us. For example, the probability that a
particular person wins first prize in a lottery may be one in a million, but
the probability that SOMEONE wins first prize is usually greater than 50%
for most lotteries. We can avoid confusion by being clear on what the
desired outcome is before the event takes place: Pr(someone wins)=1/2,
Pr(John Smith wins)=1/1,000,000.
Consider the situation in a generic ensemble theory in which every possible
outcome occurs. Clearly, Pr(some version of John Smith wins)=1. The outcome
(some version of John Smith wins) is analogous to the outcome (someone wins)
in the above example.
Now, if some version of John Smith wins, it may be argued that this is
surprising, because there is only a 1/1,000,000 probability that that
PARTICULAR version wins. But for this to be surprising, we would have to
specify the desired outcome before the event takes place: just as in the
single world example above we have to specify that a particular individual
will be the winner, in the ensemble theory we would have to further specify
that a particular version of that individual will be the winner.
The difficulty is that it is impossible to specify a particular version of a
particular individual in an ensemble theory. The different worlds do not
come labelled in any way, and it is not possible in general to pick out any
attribute which will single out a particular world or individual, because
the only necessary difference is the outcome of interest. In other words,
the only way to specify which version of John Smith will win is to specify
the outcome (that version of John Smith who will win, will win), which is
obviously not going to lead to any surprises.
Stathis Papaioannou
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Received on Tue Oct 12 2004 - 04:03:48 PDT