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If an investor operates under knightian uncertainty, does that investor then have a Bayesian viewpoint on probability implicitly, and vice versa? Has this been answered or do I have a poor understanding of one of them?

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You have a correct understanding. There is a subtle difference in that Knight effectively distinguishes uncertainty from chance. It could be argued that there is no such thing as chance in the Bayesian posterior density. To understand why, imagine that you were holding a strictly fair coin and you were going to gamble with an unknown stranger who would flip the coin.

Upon doing some research on the stranger you discover it is either Mandrake the Magician who will always be capable of controlling which side comes up, or his brother Chuck the Clueless, his identical twin brother and who know nothing about tossing coins. The chance properties of the coin matter if Chuck tosses the coin, but there are no chance properties if Mandrake does. In the absence of a mistake by Mandrake, the outcome is known. If Mandrake can make mistakes, that still isn't chance, but an incorrect application of policy.

The Bayesian posterior predictive distribution integrates out the uncertainty leaving only chance effects, but unlike Knightian uncertainty, there is no uncertainty remaining at all because the true value of the parameter is no longer a determinant of the decision process.

Now the problem with Knightian uncertainty is that I do not believe you can really operationalize it. I think you are either trapped with uncertainty or chance. I think you are either in the parameter space or the sample space. I don't think you get to be in both at the same time. I am not sure what it would mean to try and split them the way he does, except as a mental exercise. After all, Chuck might also be a magician, but he is purposefully behaving as if chance were the decider.

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