Risk v ambiguity

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So two prominent economist-types, Gary Becker and Richard Posner, have put together a blog. In their first post, they have already revealed one of the great failings of economics today: it has no means of handling ambiguity.

Definitions: risk is a situation where there are a few known probabilities--like playing the lottery. People screw up the math sometimes (e.g., they tend to round ultra-small probabilities up until they're just small probabilities), but generally do OK with it. Ambiguity is a situation where there are a number of possible outcomes, but you have only a vague idea of which will occur.

The economist approach is to turn ambiguity into risk. Posner & Becker implicitly do this by talking about expected payoffs with regard to terrorist acts, implying that we can write down the probability that the U.S.A. will suffer a terrorist act in the next week, month, or year. But there's no way to assign such probabilities. Terrorist acts are like earthquakes: there may be some fixed set of events that cause them to occur with a fixed probability, but we humans have no frigging clue what those events are, and how to turn them into probabilities.

`Oh, B', you're thinking, `you're just hairsplitting. We can't come up with a perfect estimate of probabilities, but we can try to the best of our abilities.' I used to think the same way, but there is an abundance of evidence that we humans process ambiguity and risk in truly distinct ways.

The most oft-cited is the Ellsberg paradox. In urn A, we have 51 red balls and 49 white balls. In urn B, we have 100 red or white balls, but we're not telling you how many of each. That is, A is a risky urn and B is an ambiguous urn. In experiment 1, we tell our subjects we'll give them ten bucks if they draw a red ball; they consistently choose to draw from urn A. In experiment 2, we tell our subjects we'll give them ten bucks if they draw a white ball; they still consistently choose to draw from urn A.

The standard risk-as-ambiguity model says that people just assign a risk of white ball to urn B, probably using the Principle of Insufficient Reason, which says that if you don't have any information, just call it a 50-50 chance. But there's clearly no way to assign a single white ball count to urn B that would cause you to prefer urn A in both cases--either there are more than fifty red balls in urn A or there ain't. [The terrorism issue shows parallels to this: we don't know the probability of terrorism, so no matter the true circumstances, we assume the worst, in a manner that turns out to be inconsistent with any clear view of the world. We respond to ambiguity with irrational fear; then decisionmakers set policy based on this.]

There is also some evidence (I can dig up citations on request, but brain scans are a bit questionable; if I gave the name I'd have to give critique) that our brains process risk and ambiguity differently. Ambiguity is processed in the reptilian part of the brain, some claim, where gut instinct gets formed; risk happens in the usual upper math-processing frontal lobe.

Even without brain scans, this seems sensible to me: as innumerate monkeys we faced ambiguity all the time, and only in the last few millenia have we managed to come up with means of describing risk. It's hard to come up with natural selection schemes that select only those who are most capable of matching their gut instinct with correct probabilities. If something has a small likelihood of occurring, a population may best evolve by ignoring that event entirely. This is textbook evolutionary stuff [especially if your textbook is Gintis's Game theory evolving, which I've been teaching from. He repeatedly quips that “Nature abhors low-probability events.”].

The other cause of all of this is that there is no way to prove a probability wrong. When the weatherman says that there's a 90% chance of rain, he can't be proven wrong no matter what happens tomorrow. This is especially the case with sporadic catastrophic events like earthquakes or terrorism. There's no consistent data to gather, and so no way to verifiably prove somebody right or wrong. All of the usual narrow-path yarns about how we could repeatedly trade with somebody who does the math wrong and bankrupt them, or that evolution will select them out of the population, don't apply. Ambiguity is not risk, and there's no reason to presume that one is a fair approximation of the other.

So there is no way to fit ambiguity into an expected utility calculation, since we can't just come up with our best risk estimate and call them equivalent. The result is that, frankly, economists have no way to describe an objectively correct decision procedure in the face of ambiguity. I'm not prepared to throw up my hands and say it's impossible, but right now we don't have the technology; there's a Nobel in it for whomever finds a robust ambiguity-is-not-risk way to apply narrow-path economics to ambiguous situations.

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