The fact that an "event" has some uncertainty around its magnitude carries some mathematical consequences. Some verbalistic papers still commit in 2019 the fallacy of binarizing an event in [0, ∞): A recent paper on calibration of beliefs, [14] says "...if a person claims that the United States is on the verge of an economic collapse or that a climate disaster is imminent..." An economic "collapse" or a climate "disaster" must not be expressed as an event in {0, 1} when in the real world it can take many values. For that, a characteristic scale is required. In fact, under fat tails, there is no "typical" collapse or disaster, owing to the absence of characteristic scale, hence verbal binary predictions or beliefs cannot be used as gauges.
The point can be made clear as follows. One cannot have a binary contract that adequately hedges someone against a "collapse", given that one cannot know in advance the size of the collapse or how much the face value or such contract needs to be. On the other hand, an insurance contract or option with continuous payoff would provide a satisfactory hedge. Another way to view it: reducing these events to verbalistic "collapse", "disaster" is equivalent to a health insurance payout of a lump sum if one is "very ill" –regardless of the nature and gravity of the illness – and 0 otherwise.
And it is highly flawed to separate payoff and probability in the integral of expected payoff. Some experiments of the type shown in Fig. I-5 ask agents what is their estimates of deaths from botulism or some such disease: agents are blamed for misunderstanding the probability. This is rather a problem with the experiment: people do not necessarily separate probabilities from payoffs.
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Misunderstanding of Hayek’s knowledge arguments: "Hayekian" arguments for the consolidation of beliefs via prices does not lead to prediction markets as discussed in such pieces as [25], or Sunstein’s [26]: prices exist in financial and commercial markets; prices are not binary bets. For Hayek [27] consolidation of knowledge is done via prices and arbitrageurs (his words)–and arbitrageurs trade products, services, and financial securities, not binary bets.
- Full paper by Taleb here
The point can be made clear as follows. One cannot have a binary contract that adequately hedges someone against a "collapse", given that one cannot know in advance the size of the collapse or how much the face value or such contract needs to be. On the other hand, an insurance contract or option with continuous payoff would provide a satisfactory hedge. Another way to view it: reducing these events to verbalistic "collapse", "disaster" is equivalent to a health insurance payout of a lump sum if one is "very ill" –regardless of the nature and gravity of the illness – and 0 otherwise.
And it is highly flawed to separate payoff and probability in the integral of expected payoff. Some experiments of the type shown in Fig. I-5 ask agents what is their estimates of deaths from botulism or some such disease: agents are blamed for misunderstanding the probability. This is rather a problem with the experiment: people do not necessarily separate probabilities from payoffs.
[---]
Misunderstanding of Hayek’s knowledge arguments: "Hayekian" arguments for the consolidation of beliefs via prices does not lead to prediction markets as discussed in such pieces as [25], or Sunstein’s [26]: prices exist in financial and commercial markets; prices are not binary bets. For Hayek [27] consolidation of knowledge is done via prices and arbitrageurs (his words)–and arbitrageurs trade products, services, and financial securities, not binary bets.
- Full paper by Taleb here
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