A Simple Black Swan Proof

 My recent conversation with Nassim Taleb was quite fun.  (Full audio coming soon).  Reading through Antifragile, though, I often felt like he was overcomplicating things.  Taleb is rightly annoyed when people estimate “the worst thing that can happen” using “the worse thing that has happened.”  But you don’t need non-normality or convexity or fat tails to expose this fallacy.  Indeed, you don’t need any distributional assumptions.  Why not just say this?

1. Either the worse thing ever has already happened or it hasn’t.

2. If the worst thing ever has already happened, then the badness of the worst thing ever equals the badness of the worst thing that has already happened.

3. If the worst thing ever hasn’t already happened, then the badness of the worst thing ever exceeds the badness of the worst thing that has already happened.

4. If we know with certainty that the worst thing ever has already happened, the expected badness of the worst thing ever equals the badness of the worst thing that has already happened.

5. If we don’t know with certainty that the worst thing ever has already happened, the expected badness of the worst thing ever exceeds the badness of the worst thing that has already happened.

6. We don’t know with certainty that the worst thing ever has already happened, so the expected badness of the worst thing ever exceeds the badness of the worst thing that has already happened.

Taleb is wise to warn us against using the worst thing that’s ever happened to estimate the worst thing that can happen.  But his point is a lot more general than he seems to think.  As long as you have enough common-sense to admit that the worst thing ever might not have happened yet, his warning holds.

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