In today’s Wall Street Journal Richard Posner has a commentary on the probability of catastrophe (subscription required), largely inspired by the tsunami last week and his new book, Catastrophe: Risk and Response. From the Publisher’s Weekly editorial review of the book:
Criticizing the “blinkered perspective” of civil libertarians hung up on constitutional law, he finds certain curtailments of freedom an acceptable trade-off for preventing terrorist attacks and offers a lengthy justification of torture as one such option. Posner also offers subtle insights into the psychology of disaster preparedness, noting, for example, that science fiction movies in which the world is routinely saved inure us to the possibility of facing such threats in real life, as well as create undue faith in the saving grace of scientists. And his call for increased scientific literacy among public policy leaders may be too pragmatic to fault. Though clearly not for general readers, this thoughtful analysis may trickle down from the wonkocracy.
OK. Fine. And yes, I’ve been reading the Becker-Posner blog, and Posner’s guest blogging elsewhere. I’ve read some, but not all, of his work. Yes, Posner’s a genius, and a dilletante genius at that, which I admire and respect. But I’ve been thinking this one through the whole way up to work on the train, and I can’t make heads or tails of what he means:
Why weren’t any cost-justified precautionary measures taken in anticipation of a tsunami on the scale that occurred? Tsunamis are a common consequence of earthquakes, which themselves are common; and tsunamis can have other causes besides earthquakes — a major asteroid strike in an ocean would create a tsunami that would dwarf the Indian Ocean one.
There are a number of reasons for such neglect. First, although a once-in-a-century event is as likely to occur at the beginning of the century as at any other time, it is much less likely to occur in the first decade of the century than later.
Huh? Sounds to me like Posner is saying that the probability of a natural disaster at time t, conditional on the fact that a disaster has not happened since the calendar last clicked over a century, increases at t gets farther away from the beginning of the century. Is that true? Can that be true? Do natural disasters and the rules of probability and statistics pay attention to the human calendar? Put another way, if there hadn’t been a massive earthquake in San Francisco in 1906 and another one in 1989, should the residents of the Bay Area have been quaking in their boots in 1998-2000?
Maybe he’s making a more subtle point about a rolling century, such as if something happens x times a century as expressing a probability p of its occurrence, if it hasn’t happened in the past 95 years the conditional probability of its happening in the next five years is quite high. But even that is still just a probability; it’s not certain that it will happen with proability one in the next five years.
One reason this claim jumped out at me is that I think Posner is worried about how well (or poorly) humans assess probabilities of infrequent, heretofore unknown, and/or high cost events. Sounds like he’s been reading some behavioral economics! As a counter-claim, I offer this result from some research I’ve been reading:
Cosmides Leda, Tooby John, “Are humans good intuitive statisticians after all? Rethinking some conclusions from the literature on judgment under uncertainty,” COGNITION 58 (1): 1-73 JAN 1996
Here’s the abstract of the paper:
Professional probabilists have long argued over what probability means, with, for example, Bayesians arguing that probabilities refer to subjective degrees of confidence and frequentists arguing that probabilities refer to the frequencies of events in the world. Recently, Gigerenzer and his colleagues have argued that these same distinctions are made by untutored subjects, and that, for many domains, the human mind represents probabilistic information as frequencies. We analyze several reasons why, from an ecological and evolutionary perspective, certain classes of problem-solving mechanisms in the human mind should be expected to represent probabilistic information as frequencies. Then, using a problem famous in the “heuristics and biases” literature for eliciting base rate neglect, we show that correct Bayesian reasoning can be elicited in 76% of subjects- indeed, 92% in the most ecologically valid condition- simply by expressing the problem in frequentist terms. This result adds to the growing body of literature showing that frequentist representations cause various cognitive biases to disappear, including overconfidence, the conjunction fallacy, and base-rate neglect. Taken together, these new findings indicate that the conclusion most common in the literature on judgment under uncertainty- that our inductive reasoning mechanisms do not embody a calculus of probability – will have to be re-examined. From an ecological and evolutionary perspective, humans may turn out to be good intuitive statisticians after all.
So Cosmides and Tooby find that representing probabilities as frequencies (such as “once a century”) does counter biases that humans bring to decision-making under uncertainty. It also sounds like we are not Bayesian decision-makers … this paper does not address the magnitude of the event or what happens specifically at very low probabilities, but I think because of it I am prone to take Posner’s analysis with a grain of salt and to question his imprecise articulation that I quoted above.
Note also the language that Cosmides and Tooby (who are evolutionary psychologists) use: evolutionary standard under ecologically realistic conditions, etc. This is a very different way of hypothesizing about, testing and evaluating human behavior than the Cartesian deductive logic underlying (I would claim all of) Posner’s work. When these two ways of viewing human action lead to different conclusions, it’s worth analyzing them jointly and testing them against each other. Yes, I’m being deliberately cagey there, but that’s because I’m working on something that involves this, and I’m still thinking through the articulation.