# Re: Doomsday argument & Shooting Room

Robin Hanson (hanson@hss.caltech.edu)
Thu, 12 Dec 1996 15:36:29 -0800 (PST)

I wrote:
} 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? ... I
} think you do get the bias Leslie expects, however, if you can see how
} many people are in the room with you.

Eliezer S. Yudkowsky responded:
>Say WHAT? Your chance of winning is ((1/6 + 1/36) / 2) = 7/72 or around
>9.7%. The number of people in the room has NOTHING to do with this any
>more than the number of clouds in the sky, unless you're being assigned
>to some post-hoc group.

Damien R. Sullivan responded:
>I'm not quite clear as to what analogy is being drawn. It seems to me
>that the # of people is relevant only because given the rules, it tells
>you what stage of the game you're at, which is all you want to know.

Yes, the game stage is a clue to winning chance.

>If you're early in the game, you can't tell which rule is being used; if
>you're at stage 40, it is more likely that the 1/36 chance is being used.

The two winning chances imply two different distributions over game
stage, and these distributions are only equal at most at one stage.
So everywhere else, the stage is a clue. At the first stage, the clue
is the strongest that the winning chance is high.

Robin D. Hanson hanson@hss.caltech.edu http://hss.caltech.edu/~hanson/