Most important concepts we don't teach in school: expected utility

Imagine you're talking to an insurance salesperson. She tells you that DNA testing reveals you have a 1% chance of developing a certain form of cancer which, when untreated, is always fatal. She says there is a cure, but it's so expensive no one can afford it without insurance. She hands you an insurance contract to sign; if you do, the costs of treatment, should you need it, will be fully covered so even if you do get sick you will still live. You stare at the dotted line holding a pen, then ask what your premium would be. "Oh, we don't know that yet," she says. "But we'll get back to you on that real soon." Would you still sign the contract?

Of course not; only a complete idiot would. Whether or not it's worth it to insure yourself against a 1% chance of dying depends on the premium you'd have to pay. And yet we are offered exactly the same absurd sales pitch as described above when we're being sold public policy. I'm referring to what is now known (perhaps misleadingly) as Dick Cheney's "One Percent Doctrine." The name comes from the following line from the former Vice-President:

If there's a 1% chance that Pakistani scientists are helping al-Quaeda build or develop a nuclear weapon, we have to treat it as certainty in terms of our response.

This quote contains the very same error in reasoning as the insurance deal above; and both could be remedied if more attention was paid to the concept of expected utility.

Suppose you're trying to decide whether or not to carry out some action A. If you don't do A, there's an X-percent chance you will lose a Y amount of money. If you do A, you won't lose Y; however, doing A is costly too (say it costs Z). Expected utility says you should do A if and only if Z<X*Y. In other words, you need to compare the costs of action to the costs of inaction times the probability of bad things happening due to inaction. Cheney's doctrine focuses exclusively on the likelihood of bad outcome of inaction, without trying to balance it against the costs of action.