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A one-in-a-million chance of dying.

Reasoning about probability can be complicated stuff, and from false positives in medical screening to false hopes in lotteries, it seems that very rare outcomes cause particular difficulties. The micromort (µmt), introduced by Ronald A. Howard in the '80s, provides a handy unit for comparing (and valuing) such risks.

Every day around 50 people in England and Wales die as a result of accidents or violence, which, given the total population, means that Brits face a baseline risk of about a micromort a day. 230 miles by car adds another one- as does just six on a motorbike - whilst air travel introduces about a third of a micromort per flight, which might make you wonder about all the security theatre. The argument by the chairman of the Advisory Council on the Misuse of Drugs that Ecstasy was no more risky than horse riding led to calls for his resignation, yet crunching the numbers suggests a micromort per tablet and half a micromort per ride. A better comparison might have been SCUBA diving, which weighs in at 5µmy a dive yet somehow avoids tabloid outrage; such discrepencies illustrate that there's more to our decision making processes than the raw statistics, of course.

There's also the issue of actual outcomes in terms of lives lost: although it takes 6000 miles of rail travel before you hit an extra micromort, far more people commute that way than by, say, hang gliding (8µmt a trip); so despite the relative risks, one might reasonably expect greater safety regulation of one than the other.

Take the number of vehicles in the field (A), multiply it by the probable rate of failure (B), then multiply the result by the average out-of-court settlement (C). A times B times C equals X... If X is less that the cost of a recall, we don't do one.
How much would you have to pay someone to accept a given risk level, or how much would they pay to eliminate one? (Interestingly, the two numbers start to diverge around 1000µmt.) Naturally, the phrasing and context of such a question will influence the answer: consider it posed straight, but then ask yourself how readily you'd fly on a cheaper airline with a slightly worse crash record. Howard, working for General Motors, considered actions (or rather, purchasing decisions) to speak louder than words, and based on the willingness to pay for safety features on cars a typical value seems to be around £20-25 for an extra micromort of safety.

Sources
David Spiegelhalter is Winton Professor of the Public Understanding of Risk at Cambridge University, and discussed this as part of an excellent talk I attended there in April. I later found that he has an article on it in The Times, from which most of the numbers here are shamelessly stolen.
According to Wiki, Howard's original article is On making life and death decisions (1980), whilst the £20-25 figure, adjusted for inflation and converted, comes from Microrisks for medical decision analysis (1989). Academic credentials permitting, I'll check those next time I'm in my office.

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