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.
Suppose we modify it so that you are handed a biased coin, a coin which
will come up heads or tails with 99% vs 1% probability. You know about
the bias but you don't know which way the bias is. You flip the coin
and walk into the room. Now, I think you will agree that you have a
good reason to expect that when you turn on the light, you will be in
the more crowded room. You are now a typical member of the room so the
same considerations that make one room more crowded make it more likely
that you are in that room.
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. Instead, they have an expectation of which lane they will
start in based on their long experience of driving in various conditions.
It's pretty hard to think of yourself as a typical driver given the wide
range of personality, age and experience among drivers on the road.
Hal Finney
