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From: Eric Cavalcanti <eric.domain.name.hidden>

Date: Fri, 01 Oct 2004 10:36:53 +1000

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

Date: Fri, 01 Oct 2004 10:36:53 +1000

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.

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.

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

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