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.

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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.