Thursday, August 20, 2009

When judges are bad at arithmetic

Richard Posner is a very smart man who enjoys feigning expertise even when he has little understanding of the topics at hand. Mark Thoma, Brad DeLong, and Menzie Chinn provide some well-deserved criticism of his latest; DeLong notes that Posner missed the appropriate comparison between stimulus money and GDP change by a factor of sixteen. (!)

Posner's lack of facility with arithmetic comes as little surprise. It's a defining feature of his commentary, and was thrown into particularly sharp relief for me when he opined on drunk driving back in 2006:
This is actually a plausible inference. If there are only 2,000 nonpassenger deaths (other than that of the drunk driver himself) caused by drunk driving every year (and how many of the accidents in which a drunk driver is involved are actually caused by the drinking?), then the probability of being killed by a drunk driver is very small...
The second parenthetical comment is utter nonsense—a clever debater's jibe that cannot hold up to even the slightest quantitative scrutiny. Consider the fraction of traffic fatalities associated with drunk driving: about a third, according to the NHTSA. Now imagine the number of miles driven drunk as a fraction of the total vehicle miles in the United States. When you consider that most Americans do not drive over the legal limit, and even those who do drive drunk generally do so for only a small fraction of their total driving time (much of which consists of routine driving like the daily commute), it's hard to imagine that this ratio is any more than one in a thousand.

If, say, 30% of deaths associated with drunk driving are not actually caused by drunk driving, it follows that the kinds of people who drive drunk must be at least a hundred times more likely to cause a fatality when driving as the rest of the population. Granted, I am sure that the ratio is more than one, but I very much doubt it is anywhere near 100.

You can quibble with my assumptions if you like. No matter how you slice the numbers, however, it is impossible to describe a world where more than a small fraction of deaths involving drunk driving would have occurred without it. Yet this analysis clearly never occurred to Posner. He is a clever writer and debater, but he lacks the quantitative intuition that makes such insights obvious. And while this isn't so bad for a judge, it's a serious problem for anyone who purports to be an authority on all matters economic.

1 comment:

stupid boy said...

Hey, I believe that Posner is not that good concerning arithmetics, but I still don't get your example. Could you clarify your reasoning?! Thanks,