official nonsense

The background is that I went to the Boston RMV to apply for a learner's permit. I had to go through the driver's manual. Unfortunately, there is some statistical non-sense in the manual that annoys me greatly.

In order to convince drivers to wear safetybelt all the time, they say "Most motor vehicle crashes happen within 25 miles of home. In fact eight out of every ten accidents occur when drivers are going 40 mph or less".  The problem of this sentence is that it is irrelevant and misleading. This is what is called a prosecutor's fallacy (http://en.wikipedia.org/wiki/Prosecutor's_fallacy). The idea is the the probability of event A given B could be very different from the probability of event B given A.  Whether we want to wear a seatbelt is dependent on the probability of having an accident conditional on we are only driving within 25 miles of home.  If that is too low to justify the cost of putting on a seatbelt, a rational person might decide not to. However, we are not interested in the probability of being within 25 miles of home given an accident happen. Reductio ad absurdum, Imagine a world where everyone drives within 25 miles of home. Even if the accident rate is negligible (less than the accident rate of air plane), we can still claim that most (actually in this case, all) motor vehicle crashes happen within 25 miles of home.

I completely understand that the intention of RMV is good--to convince people to wear safety belt. But good intention does not justify ignorance/stupidity or outright misleading. (I myself have lots against the compulsory seat belt wearing thing, as I think it makes the road less safe, but that is a topic for another day)

Prosecutor's fallacy is rampant, to my dismay. Let me digress and point out how prevalent it is. The Phi Beta Kappa society, which claims itself to be an elite society, points out that "Since inception, 17 U.S. Presidents, 38 U.S. Supreme Court Justices, and 136 Nobel Laureates have been inducted members." seems likes a high percentage for a lay person? Not really? I have an even better number. All  of US presidents, US Supreme Court Justics, and Nobel Prize winners are human beings!!! So the right thing to consider is what is the probability of doing great things given a PBK membership? Probably pathetically low. My fellow PBKs, I do not think you have any reason to register any pride with this society. 

Back to RMV. When I entered RMV at 11:51. I got a slip saying that the estimated waiting time is 14 min. I thought to myself, great!!! Then I was called when it was past 13:00. I doubt if takes super advanced statistics to get a slightly more accurate estimates.