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The Weight of Probability, the Cloud of Uncertainty, and More

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  1. A.J. Sutter says:

    Thanks for your reply. As for your point about settlement rather than adjudication, yes, of course. I also agree that we wouldn’t know the probability of success of a home office deduction or other common transaction in a frequentist sense. For that reason, though, I’m not sure I buy your distinction between risk and uncertainty aversion in the case of fancy tax shelters either. When you say that a wealthy taxpayer might not want to roll the dice “if he doesn’t know what the odds are” begs the question of whether the odds are knowable. But since most rich folks probably don’t read this blog, maybe what matters more is whether they *feel confident* that they “know the odds;” they probably don’t know that the odds are unknowable a priori. In that case “risk” would be a subjective state too.

    If it were me getting the tax advice, and I were thinking in such highfalootin’ terms at all, I’d probably consider the adviser’s basis for estimating prior probabilities — i.e., I’d be thinking in a more Bayesian vocabulary. (You hint at this with your Keynesian characterization.) I’d also be considering other chunks of information to form my own subjective probability estimates of whether the adviser is trustworthy, e.g., how many years’ experience does he or she have, is he wearing a pinkie ring, etc.

    As I mentioned in a comment to an earlier post, the notion of “risk” seems like a bit of a straw man or foil, a point of comparison for contrasting an excessively theoretical approach with a real life one favored by the person making the distinction. It’s worth noting that even Kolmogorov, who created the modern measure-theoretical foundations of probability theory (which are also frequentist), waved his hands about the application of probability to reality, at least in situations other than highly controlled, laboratory conditions. See, e.g., Jan von Plato’s _Creating Modern Probability_ (Cambridge UP 1994) @ 219-221.

    I admit I’m being something of a stickler in insisting on the rarity of true risk in everyday life. In an earlier post, you defend the distinction by saying that “Some things operate more like known probabilities, and some things operate more like unknown probabilities — that is, some things are more risky (e.g., coin flipping), and some things are more uncertain (e.g., presidential elections).” You make it sound like more of a fuzzily-defined difference in degree, rather than in kind; that might be OK for informal, colloquial use. And the way Frank Knight used it may have been fine, given his polemical purpose. But this raises the question of whether Knight’s distinction is really as profound as people make out when they try to use it in other contexts. You don’t need his distinction to distinguish frequentism from subjectivism, or to see the subjectivity of many probability estimates. On the other hand, his distinction can be misleading if it becomes reified and interpreted as something more rigorous than it is.

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