# The three door problem on the road:

sonhouse
Posers and Puzzles 20 Jun '12 14:53
1. sonhouse
Fast and Curious
20 Jun '12 14:53
So you are driving on a three lane one way road and you see a traffic jam. Does it do any good to change lanes, that is to say, is there a tactic you can use like the 'what's behind the three doors' game, where you make a guess and then get a second guess, do you stay where you are or change lanes?
2. 21 Jun '12 12:37
Originally posted by sonhouse
So you are driving on a three lane one way road and you see a traffic jam. Does it do any good to change lanes
No. Even if there is a mathematical theory that predicts there is, human (and particularly automobilistic) perversity means that nothing you do is likely to help in practice. In fact, it is a well-documented fact that too many people changing lanes in the hope of getting one up on their "fellow" drivers do, in fact, cause the jam to worsen.

Richard
3. 21 Jun '12 20:18
Originally posted by Shallow Blue
No. Even if there is a mathematical theory that predicts there is, human (and particularly automobilistic) perversity means that nothing you do is likely to help in practice. In fact, it is a well-documented fact that too many people changing lanes in the hope of getting one up on their "fellow" drivers do, in fact, cause the jam to worsen.

Richard
..."it is a well-documented fact that too many people changing lanes in the hope of getting one up on their "fellow" drivers do, in fact, cause the jam to worsen."

Supposing this is true; that numerous lane changers causes a jam to worsen, then the rational driver will at first conclude that if everyone stays in their lane, they will all be better off, including him.

But then a lone lane-changer in a jam full of non-lane changers may benefit more than the average non-lane changer does.

This is similar to the game theory conclusion that in some situations, solo defectors can benefit from a situation that they would not benefit from if everyone defected.

As an RHP example, the solo machine user in a tournament may benefit (may win the tournament) but if everyone used one, he wouldn't. Similarly, the solo sandbagger (ie, who purposely lost games to lower his score) who entered a banded tournament would benefit, but if everyone in the tournament had sandbagged, he wouldn't benefit.

But back to the lane changer: The solo lane changer still needs some lane-changing rules.
4. 21 Jun '12 23:14
You might be able to make some headway if the lanes are moving erratically:

If the lanes are moving at the same speed, force yourself into the middle lane.
If a lane is moving faster than you, force your way into it.

You would get beeped a lot doing that here in the uk though, unless on a motorbike. Personally I try to close up gaps and drive parallel to drivers doing this in jams so they can't switch.
5. forkedknight
Defend the Universe
22 Jun '12 04:41
Originally posted by iamatiger
Personally I try to close up gaps and drive parallel to drivers doing this in jams so they can't switch.
You're just one of the many dicks on the road, then.

If all drivers were to always allow anyone that signaled to merge in front of them, everyone would benefit from faster traffic flow.

I try to do by part.
6. 24 Jun '12 18:42
Merging is ok, if they take turns, repeated switching back and forth to gain a few cars length slows everyone behind down and is bad.
7. sonhouse
Fast and Curious
24 Jun '12 19:37
Originally posted by iamatiger
Merging is ok, if they take turns, repeated switching back and forth to gain a few cars length slows everyone behind down and is bad.
On my actual commute, Interstate 78 in PA and NJ and interstate 287, it seems obvious everyone drives too fast. They get up to 80 mph, ~130 klicks, and everything seems to be going smoothly till the first slowdown, then they are all packed together doing 30 again. It seems to me if they all drove just the speed limit there would be more time for the whole crowd to continue at that speed for a much longer time since being slower would not be packing cars up so much when there is a slow down, the slow down would have a better chance to work itself out before the large crowd of cars arrives.
8. 25 Jun '12 09:01
Originally posted by JS357
..."it is a well-documented fact that too many people changing lanes in the hope of getting one up on their "fellow" drivers do, in fact, cause the jam to worsen."

Supposing this is true; that numerous lane changers causes a jam to worsen, then the rational driver will at first conclude that if everyone stays in their lane, they will all be better of ...[text shortened]...
But back to the lane changer: The solo lane changer still needs some lane-changing rules.
So now it's a prisoner's dilemma?
9. 25 Jun '12 12:18
Originally posted by Vartiovuori
So now it's a prisoner's dilemma?
No, but (too) many drivers believe it is.

Richard
10. 25 Jun '12 16:012 edits
Originally posted by Vartiovuori
So now it's a prisoner's dilemma?
It seems more like a situation where it is rational to be the lone lane-changer (or among a few of them) but if SB is right that mass lane changing makes jams worse, and if every driver says OK I'll be a lane changer, it will defeat the strategy, most if not all will lose.

Once in my life I had a car honking to get by and the driver pulled alongside when I let him, and thanked me, hollering that they were on the way to have a baby. This was a block from the hospital and they did pull in to it.

This is similar to any situation where a good is made available to those who need it, leaving the decision as to whether they need it to them -- then everyone decides they "need" it. Is there a game theory paradigm for this? The tragedy of the commons?

"The tragedy of the commons is a dilemma arising from the situation in which multiple individuals, acting independently and rationally consulting their own self-interest, will ultimately deplete a shared limited resource, even when it is clear that it is not in anyone's long-term interest for this to happen." -- WIkipedia

So if we knew that people only wanted to lane jump it in an emergency, we'd let them. They'd benefit greatly with minimal cost to us. But no, too many people act like other drivers are just a nuisance to their important lives, instead of like partners in an activity they can optimize by cooperation and restraint.
11. sonhouse
Fast and Curious
29 Jun '12 15:18
Originally posted by JS357
It seems more like a situation where it is rational to be the lone lane-changer (or among a few of them) but if SB is right that mass lane changing makes jams worse, and if every driver says OK I'll be a lane changer, it will defeat the strategy, most if not all will lose.

Once in my life I had a car honking to get by and the driver pulled alongside when I ...[text shortened]... instead of like partners in an activity they can optimize by cooperation and restraint.
One thing about that: there is coming a time when the cars will drive themselves and probably respond to traffic computers which would issue speed suggestions, say a message comes in, slow down to 80 klicks and a coming jam will be avoided.

That is the only practical way to ensure maximum traffic flow, a central computer that knows the real time traffic conditions and issuing suggestions and with human drivers who may or may not follow said suggestions.

Traffic computers can alleviate a lot of these kind of problems by being an overseer watching conditions ahead and behind, issuing messages about traffic accidents 3 klicks down the road, please get off at exit 34 and follow this re-entry route. That kind of thing.
12. 04 Jul '12 01:04
On the M25 ring motorway around London there are adaptable speed cameras which, when traffic is busy, enforce a changing speed limit which is supposed to be one that the cars can all drive smoothly at. It works quite well.
13. Pianoman1
Nil desperandum
04 Jul '12 05:48
Originally posted by iamatiger
On the M25 ring motorway around London there are adaptable speed cameras which, when traffic is busy, enforce a changing speed limit which is supposed to be one that the cars can all drive smoothly at. It works quite well.
The M25? You mean the out of town car park.
14. 04 Jul '12 10:37
Originally posted by Pianoman1
The M25? You mean the out of town car park.
It is the dread sigil Odegra, which means "Hail the Great Beast, destroyer of worlds!" Every driver on it, cursing as he goes, takes part in a massive evil prayer wheel, like a virtual Lama in the dark priesthood of Ancient Mu.

Richard
15. SwissGambit
Caninus Interruptus
04 Jul '12 14:24
Originally posted by sonhouse
One thing about that: there is coming a time when the cars will drive themselves and probably respond to traffic computers which would issue speed suggestions, say a message comes in, slow down to 80 klicks and a coming jam will be avoided.

That is the only practical way to ensure maximum traffic flow, a central computer that knows the real time traffic ...[text shortened]... cks down the road, please get off at exit 34 and follow this re-entry route. That kind of thing.
Plus, just think of the interesting stories we'll hear when there is a bug in the software. ðŸ˜€