Ambrosini Archive

Do we care about higher moments?

2008-05-29 · Original WordPress address

Government policies have stochastic effects. In particular cases, a policy can lead to government action that is extremely bad. In other cases, that same policy can lead to unmitigated good. In choosing policy, its seems reasonable to choose those where the good outcomes in some sense out weigh the bad ones. Its not obvious, though, how to weigh good versus bad outcomes. Do 10 decent outcomes outweigh one terrible outcome? Does one really great outcome outweigh 10 mediocre bad outcomes? David Friedman gives an explicit formula for choosing policy:
[I]n order to defend giving government the power to do something, you must argue not only that it can sometimes do good but that, on net, it can be expected to do more good than harm.
That is to say, choose policies such that the average outcome is positive. Suppose "mediocre bad" policy outcomes are -1 bad and one "really great" outcome is 11 good ((How to measure these outcomes is a different topic entirely... just suppose we can do so.)). The average of these outcomes is positive, so the policy that produced them should be implemented. On the other hand if "decent" outcomes are +1 good and "terrible" outcomes are -100, the average is negative and the policy shouldn't be implemented. The problem with this method for choosing policy is that it doesn't take into account the fact that we may really hate bad outcomes relative to quantitatively equal, but positive, good outcomes. In other words, the optimal policies may be ones that avoid "terrible" outcomes entirely or makes them really unlikely. This will mean there are some policies that have positive average outcomes, but that we'd still not like. Let me make a stark example: Friedman's formula would suggest indifference between these two policies in a community of 100 people and his method suggests both should be implemented:
  1. Policy 1: one random member of the community is killed, but the rest of us get $101,011 ((Here I'm assuming the statistical value of a life is $10m. I think the normal estimates are between $2m and $10m, but I'm too lazy to look it up.)).
  2. Policy 2: Everyone gets a check for $0.89
Given certain assumptions about the value of a statistical life, these two policies have the exact same value in expectation. Problems?

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