The Yom Kippur effect

October 1, 2009 in Economics,Math

You may have noticed a minor obsession with traffic amidst TGR's usual fare, which is why I was especially interested in a recent Freakonomics piece called "A Gut Yontif for L.A. Drivers" (Gut Yontif is a traditional Yiddish greeting used on Yom Kippur - it literally means "good holiday"). The post's motivation is purely anecdotal - so all the usual disclaimers apply - but its conclusion is nonetheless instructive:

There’s a big improvement in the Westside traffic situation every year on the Jewish high holidays. To many, this seems mysterious. True, West L.A. and the southern San Fernando Valley have large Jewish populations, but not that large. How can the removal of a relatively small number of cars be responsible for such a marked drop in congestion?

The reason is the non-linear way in which traffic congestion builds.

The argument goes like this: start with a road. That road can handle a certain number of cars, c (analogous to the amount of water that can flow through a bottleneck in a given space of time).  So long as the actual number of cars n is less than c, traffic flows smoothly. For example, if n = 1, that driver can go as fast as he wants. As n grows, the drivers must drive more slowly and carefully to avoid collisions. When n = c, there are so many drivers that at least one car is not moving at any moment.

Adding one more car at this point will not just result in an additional stalled vehicle - that car will cause the car behind it to stop, and so on. The next additional car will further compound the problem, and every marginal car thereafter will disproportionately cause more traffic to stop. Refer to this video for scientific proof.

The final important factor is that there is some level m which is the maximum number of cars that can fit on a road (as in, physically). In a perfect, computer controlled world, c = m; in real life c is somewhat less than m, but probably not dramatically so because once a road is at traffic capacity, there simply isn't room for many more cars.

The proportion p of traffic-causing drivers is given by

p = \frac{\max(n-c\;,0)}{n}, \;\;\; n\leq m

and it follows that p can be no larger than the amount by which m exceeds c. I think a reasonable upper bound for p would be around 10%.

Given that L.A. roads frequently exhibit n > c (in other words, L.A. traffic is terrible), and that n can only exceed c by a small amount, the argument follows that removing only a few cars (specifically, p% of them) will restore traffic to normalcy. The Jewish population of L.A. is about 4% of the MSA's total population (this number divided by this one), so if any substantial proportion of them are off the roads on Yom Kippur, it really could make a substantial difference.

Concretely, Freakonomics notes that if this outcome is really true, it "augurs well for solutions like congestion pricing... because if dissuading only a few drivers will make a significant difference, the tolls may not have to be draconian."

Of course, my whole analysis assumes that the population is otherwise homogeneous. It's also possible that a small number of observant Jews are just awful drivers and getting them off the road makes traffic flow fine - but I've had enough crazy theories already this week.

Notably, there is also a Yom Kippur effect on stocks - traded volume is unusually low during the holiday. For more detail see this 2003 paper (pdf).

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