Eric Cavalcanti writes:

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.

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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