From: Robin Hanson (hanson@hss.caltech.edu)
Date: Tue Dec 10 1996 - 16:33:34 MST
Posters here have effectively convinced me that, given the
assumptions of Hal's shooting room problem, I should expect a 1/36
chance of seeing double-sixes condition on being in the room.
Thank you all for your clear thinking.
This problem is an explicit counter-example to the doomsday argument.
That is, there are things one could know such that the doomsday
argument shouldn't concern one. Doomsday argument proponent John
Leslie, however, explicitly acknowledges this fact, and counters with
the claim that we are not in such a state of knowledge.
Leslie is confused about why exactly this shooting room problem is a
counter example - he thinks it has something to do with
"non-determinism", which I think is just sloppy thinking. (And since
Leslie thinks this type of issue is not modelable with Bayesian
reasoning, this is his excuse for not offering exact Bayesian
calculations for his arguments.) But Leslie is probably right in
saying that his Doomsday argument may have punch, given our actual
state of ignorance.
Consider the case where we are a priori uncertain about the rule used
to say if the room occupants win. There is a 50/50 chance that they
win on double sixes, and a 50/50 chance they win on any double. You
can't tell which rule is being used, even when you go into a room.
Now what odds should you assign to winning?
The doomsday argument says it should be much nearer to 1/6 than to
1/36. Yet if you don't know how many people are in the room with you,
I think it would have to be nearer to 1/36, the opposite bias! I
think you do get the bias Leslie expects, however, if you can see how
many people are in the room with you. (Anyone want to work through
the details?)
Robin D. Hanson hanson@hss.caltech.edu http://hss.caltech.edu/~hanson/
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