Why cars in the next lane do go faster
Department of Philosophy, Yale University, New Haven, CT 208306, USA
Do the cars in the next lane on the motorway go faster than the cars in your own lane? According to a recent view1,2, drivers suffer from systematic illusions causing them to mistakenly think that that is the case. Here we show that this result fails to take into account an important observational selection effect. Cars in the next lane actually do go faster.
In a recent paper in Nature, Redelmeier and Tibshirani present some evidence that drivers on Canadian roadways (which don’t have an organized laminar flow) think that the next lane is typically faster. The authors seek to explain this phenomenon by appealing to a variety of psychological factors. For example, “a driver is more likely to glance at the next lane for comparison when he is relatively idle while moving slowly”; “Differential surveillance can occur because drivers look forwards rather than backwards, so vehicles that are overtaken become invisible very quickly, whereas vehicles that overtake the index driver remain conspicuous for much longer”; and “human psychology may make being overtaken (losing) seem more salient than the corresponding gains”. The authors suggest that educating drivers about these effects may encourage them to resist small temptations to switch lanes, thereby reducing the risk of accidents.
While all these illusions might indeed occur, there is a more straightforward explanation of the phenomenon. It goes as follows. One frequent cause of why a lane (or a segment of a lane) is slow is that there are too many cars in it. Even if the ultimate cause is something else (e.g. road works) there is nonetheless typically a negative correlation between the speed of a lane and how densely packed are the vehicles driving in it. That implies that a disproportionate fraction of the average driver’s time is spent in slow lanes. If you think of your present observation, when you are driving on the motorway, as a random sample from all observations made by drivers, then chances are that your observation will be made from the viewpoint that most observers have, which is the viewpoint of the slow-moving lane. In other words, appearances are faithful: more often than not, the “next” lane is faster!
Even when two lanes have the same average speed, it can be advantageous to switch lanes. For what is relevant to a driver who wants to reach her destination as quickly as possible is not the average speed of the lane as a whole, but rather the speed of some segment extending maybe a couple of miles forwards from the driver’s current position. More often than not, the next lane has a higher average speed at this scale than does the driver’s present lane. On average, there is therefore a benefit to switching lanes (which of course has to be balanced against the costs of increased levels of effort and risk).
Adopting a thermodynamics perspective, it is easy to see that (at least in the ideal case) increasing the “diffusion rate” (i.e. the probability of lane-switching) will speed the approach to “equilibrium” (i.e. equal velocities in both lanes), thereby increasing the road’s throughput and the number of vehicles that reach their destinations per unit time.
The mistake one must avoid is ignoring the observational selection effect residing in the fact that when you randomly select a driver and ask her whether she thinks the next lane is faster, more often than not you will have selected a driver in the lane which is in fact slower. When we realize this, we see that no case has been made for recommending that drivers change lanes less frequently. The theory of observational selection effects is a relatively recent development that may have implications in a number of other fields.3 One example is evolutionary biology, where observational selection effects must be taken into account when addressing questions such as what is the probability of intelligent life developing on any given earth-like planet.4 Another example is cosmology, where observational selection effects are crucial considerations in deriving empirical predictions from so-called multiverse theories according to which our universe is but one out of a vast ensemble of physically real universes out there.5,6,7
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Redelmeier, D. A., Tibshirani, R. J. Nature 401: 35 (1999).
Redelmeier, D. A., Tibshirani, R. J. Chance 13(3): 8-14 (2000).
Bostrom, N. Obervational Selection Effects and Probabilty. (Doctoral dissertation, London School of Economics, London, 2000). (Also available at www.anthropic-principle.com/phd/)
Carter, B. (1983). Phil. Trans. R. Soc. A 310: 347-363.
Linde, A., Mezhlumian, A. (1996). Phys.Rev. D 53: 4267-4274.
Hawking, S., Turok, N. Physics preprint archive: hep-th/ 9802030 (1998).
Leslie, J. Universes (Routledge, London and New York, 1996).