Eric Cavalcanti writes:
QUOTE-
And this is the case where this problem is most paradoxical.
We are very likely to have one of the lanes more crowded than
the other; most of the drivers reasoning would thus, by chance,
be in the more crowded lane, such that they would benefit from
changing lanes; even though, NO PARTICULAR DRIVER would benefit
from changing lanes, on average. No particular driver has basis
for infering in which lane he is. In this case you cannot reason
as a random sample from the population.
-ENDQUOTE
I find this paradox a little disturbing, on further reflection. You enter
the traffic by tossing a coin, so you are no more likely to end up in one
lane than the other, and you would not, on average, benefit from changing
lanes. Given that you are in every respect a typical driver, what applies to
you should apply to everyone else as well. This SHOULD be equivalent to
saying that if every driver decided to change lanes, on average no
particular driver would benefit - as Eric states. However, this is not so:
the majority of drivers WOULD benefit from changing. (The fact that nobody
would benefit if everyone changed does not resolve the paradox. We can
restrict the problem to the case where each driver individually changes, and
the paradox remains.) It seems that this problem is an assault on the
foundations of probability and statistics, and I would really like to see it
resolved.
Stathis Papaioannou
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Received on Sun Oct 03 2004 - 20:45:41 PDT