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MichaelBishop comments on Open Thread June 2010, Part 3 - Less Wrong
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This is a good point. What happens in this individual case would be dominated by random facts about the individuals directly involved. If you imagine the same situation repeated many times, 100 should be plenty, the randomness cancels out.
So you might think. Sensitivity to initial conditions!
care to explain why we should expect sensitivity to initial conditions to matter in the particular example being discussed here?
I am struggling to convey this, so I'll have to think about it more.
For now, though: I do think that differences in the initial conditions would be propagated by adaptive individuals and institutions (rather than smoothed away). That should lead to bifurcations and path dependencies that would generate drastically different outcomes. Enough that averaging them would be meaningless.
Why do you think repeating it many times would converge? Are the statistical limit theorem conditions really met? I don't think so..
None of this really explicitly says that you wouldn't be able to at least figure out the sign of the change. It might be computationally intractable but qualitatively determinable in special cases.