Hal Finney writes:
>Stathis Papaioannou writes:
> > Here is another example which makes this point. You arrive before two
> > adjacent closed doors, A and B. You know that behind one door is a room
> > containing 1000 people, while behind the other door is a room containing
> > only 10 people, but you don't know which door is which. You toss a coin
>to
> > decide which door you will open (heads=A, tails=B), and then enter into
>the
> > corresponding room. The room is dark, so you don't know which room you
>are
> > now in until you turn on the light. At the point just before the light
>goes
> > on, do you have any reason to think you are more likely to be in one
>room
> > rather than the other? By analogy with the Bostrom traffic lane example
>you
> > could argue that, in the absence of any empirical data, you are much
>more
> > likely to now be a member of the large population than the small
>population.
> > However, this cannot be right, because you tossed a coin, and you are
>thus
> > equally likely to find yourself in either room when the light goes on.
>
>Again the problem is that you are not a typical member of the room unless
>the mechanism you used to choose a room was the same as what everyone
>else did. And your description is not consistent with that.
>This illustrates another problem with the lane-changing example, which
>is that the described mechanism for choosing lanes (choose at random)
>is not typical. Most people don't flip a coin to choose the lane they
>will drive in.
Yes, this is correct. The "typical observer" must be typical in the way he
makes the choice of room or lane. With the traffic example, given that there
are slower and faster lanes on most roads, even in the absence of road works
or accidents, this may mean that for whatever reason the typical driver on
that day is more likely to choose the slower lane on entering the road. If
this is so, then a winning strategy for getting to your destination faster
could be to pick the lane with the most immediate appeal, then reflect on
this (having participated in the present discussion) and choose a
_different_ lane. This is analogous to counter-cyclical investing in the
stock market, where you deliberately try to do the opposite of what the
typical investor does.
But there may be a problem with the above argument. Suppose everyone really
did flip a perfectly fair coin to decide which lane of traffic to enter. It
is then still very most that one lane would be more crowded than the other
at any given time, purely through chance. Now, every driver might reason,
"everyone including me has flipped a coin to decide which lane to enter, so
there is nothing to be gained by changing lanes". However, most of the
drivers reasoning thus would, by chance, be in the more crowded lane, and
therefore most would in fact be better off changing lanes.
--Stathis Papaioannou
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Received on Sun Oct 03 2004 - 02:58:02 PDT