Monday, 28 December 2009

Calculated risks

Nate Silver over at FiveThirtyEight runs the kind of back-of-the-envelope calculation on the risks of being in a hijacked aircraft that you might expect as part of a McKinsey interview.
There were a total of 674 passengers, not counting crew or the terrorists themselves, on the flights on which these incidents occurred. By contrast, there have been 7,015,630,000 passenger enplanements over the past decade. Therefore, the odds of being on given departure which is the subject of a terrorist incident have been 1 in 10,408,947 over the past decade. By contrast, the odds of being struck by lightning in a given year are about 1 in 500,000. This means that you could board 20 flights per year and still be less likely to be the subject of an attempted terrorist attack than to be struck by lightning.
What's the most you'd pay for insurance against a 1 in 10.4 million event? Since the value of a statistical life, backed out of these kinds of calculations, is $7 million, our best guess is that folks would be unwilling to spend more than a dollar to insure against this risk. I get the feeling that the TSA's budget is considerably more than that.

Ok, class: Assume that if you reduce TSA spending by an order of magnitude the risk of a terrorist incident also rises by an order of magnitude. By how many orders of magnitude ought the TSA budget be reduced to get spending to a level commensurate with the estimated risks?


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  2. "By how many orders of magnitude ought the TSA budget be reduced to get spending to a level commensurate with the estimated risks?"

    Won't the answer depend on our risk aversion?

    I wonder whether the budget is in line with the risks given the kind of people making the decision here. Politicians don't just consider the risk to our lives and limbs given a terrorist attack, but the risks to their popularity if they aren't seen to be doing *something* aimed at reducing the first kind of risk. If politicians put more weight on the second kind of risk than the first, and if they are risk averse, then to them the budget might well be justified.

    Oddly, given that the actual risk to life and limb is so small, encouraging politicians to place more decision-making weight on that than the political risks to themselves should make them want to decrease the budget. Nevertheless, it's likely that the more the public pushes home this point, the more politicians look at the second kind of risk and then continue to up budgets.

  3. So long as risk aversion is constant across the different ways you can die, it doesn't matter: VSL is then $7 million.

    I totally agree that the political costs of some deaths are higher than for others though; that's why the FDA weighs deaths from mistakenly approved drugs so much more heavily than deaths from drugs unnecessarily held from the market.

  4. I think you'd be better off approaching the issue from a diminishing returns for the government by marginal prevention and next-best strategies for terrorists. There's a point where the marginal value of a dollar goes from 'helps' to 'doesn't help at all', and we're well over that curve.

    In my mind, it's like watching a car plunging over a cliff and discussing where exactly he should have stopped.

  5. Diminishing returns does indeed strengthen the argument: shifting resources from TSA to other more poorly funded risk-reducing policies then saves lives. But that's one of the things you can find pretty easily by applying the VSL threshold: some things we're spending billions of dollars per statistical life saved; other things, tens of thousands. Shifting resources from the former to the latter saves lives.