In a recent Discord thread @dvdjsph , my grad students and I got into theoretical weeds about fat tails, etc. in the interests of prototyping David’s Promise Protocol. To give a flavor, I’ll repost here a couple sections posted by me in the context of much back-and-forth discussion.
”This from a technical footnote in: Nassim Nicholas Taleb. (2022). The Black Swan : the impact of the highly improbable. Random House Trade Paperbacks. (p. 353) "With probability simply, a metaprobability assigns degrees of credence to every probability. … " The full note is long, but all this is from a technical paper referencing, among others the work of Russell and Tarski on why sentences cannot contain their own truth predicates. (“This sentence is true” results in paradoxes). So every language needs a metalanguage. From that, Taleb derives that every probability (i. e. Credence) needs its own probability (i. e. Confidence). Bottom line - all of this is deep in the weeds white paper fodder allowing us to frame PP in very sophisticated terms.”
”Your final paragraph is Taleb in a nutshell. I came to a similar conclusion last night - for risk analysis and/or decision support, there has to be a payoff term. Most of Taleb’s energy goes into what you call k. He criticizes what he calls the “ludic fallacy”, which is applying Gaussian statistical analysis to p, assuming we really understand the rules of the game (as if life were as tidy as a casino). The Black Swan question is “what really is the game”? Long Term Capital Management, Lehman Brothers, etc. were optimizing for what they thought the game was. Taleb was hedging that the “game” was beyond comprehension and subject to adverse outcomes for unexpected reasons. So there is the probability. And there is also the probability about how right you are about the probability. And finally, the payoff (or penalty) attached to being wrong about either”
All that clearly relates, @JonahW to your latest. For any question that matters about social analysis, given some variable, is the distribution Gaussian (bell curve) or Power Law? In Taleb’s quantitative technical work, he and coauthors show very interestingly that the Power Law can derive from a Gaussian of a Gaussian. Any given data set can fit any number of bell curves! Are we all clustered around some regular center? Or we really off more in some chunking fat tail? Taleb’s point - supported rather elegantly by Promise Protocol, is for any given probability analysis, we also ought to be factoring in the probability that we may be wrong about the probability space we think we are in!