I have read some stuff on Nick Bostrom's page
(
http://nickbostrom.com/) and while in general
I agree with his conclusions about
observation-selection effects, there is one
example which I am not sure I understand.
It is the one about cars in the next lane going
faster:
(
http://plus.maths.org/issue17/features/traffic/index.html)
I agree with the general conclusion:
"when we randomly select a driver and ask her
whether she thinks the next lane is faster, more
often than not we will have selected a driver from
the lane which is in fact slower and more densely
packed."
And in a sense I agree with:
"If you are driving on the motorway and think of
your present observation as a random sample from
all the observations made by all the drivers, then
chances are that your observation will be made from
the viewpoint that most drivers have, which is the
viewpoint of the slow-moving lane."
That is, IF I think of my present observation as a
random sample from all the observations, THEN chances
are that my observation is from the slow lane. But
I am not sure I agree that we can always think of
our observation as being from such a sample.
For example: suppose I just arrived at a 2-lane
road. I took lane A. One of them is slower than the
other, in the sense that for the next couple of miles
after my initial positioWhere is the flaw?
n the average velocities of
the cars in lane S is lower than on lane F. But it is
not clear which (A or B) is faster from my point-of-view
(POV), so that, in trying to decide which lane to go,
I need to think of a statistical argument to decide
wether or not I should change lanes.
>From Bostrom's argument, I should think of my observation
as being selected from a sample of the drivers on the
road, so that it is more likely that I am on the slower
road. Therefore, I should change to lane B.
>From another perspective, I have just arrived at the
road and there was no particular reason for me to
initially choose lane A or lane B, so that I could just
as well have started on the faster lane, and changing
would be undesirable. From this perspective, there
is no gain in changing lanes, on average.
Extending the argument, suppose I drive for a couple
of miles, and get to another point where I want to decide
if I should change lanes. Since I had no reason to
change lanes a couple of miles ago, I still have no reason
to do so now. Unless, of course, I can clearly see that
the next lane is faster, but adding that assumption changes
the problem completely.
Where is the flaw?
Eric.
Received on Thu Sep 30 2004 - 20:41:32 PDT