There is, as de Finetti said, no such thing as probability. So there is no such thing as risk, either, since risk relies upon probability.
If there is no such thing as risk, which there isn’t, then why does it seem to make sense to say people are mis- or wrongly estimating risk? For the same reason it seems to make sense to say people mis- or wrongly estimate probability.
For instance, I say that the average middle-aged New York City streetwalker (don’t even bother telling me) is far more fearful than she should be about dying, or even unduly suffering, from coronadoom. But this criticism can’t be right if risk does not exist.
Of course, if risk doesn’t exist, then our lady has no reason to think one way or the other about the virus, let alone worry about any other thing that might cause her harm. Yet since worrying about certain dooms, like climbing a mountain without a rope, also makes sense, it seems risk does exist. And if risk exists, so must probability.
The solution to this mini-dilemma for risk is the same as for probability, and that is to recognize that there is no such thing as unconditional probability, thus there is no such thing as unconditional risk. Both risk and probability are epistemic, matters of what you know. They do not directly speak of the way the world is, but in what you know about the world. All probability, and so all risk, is conditional on the evidence assumed.
It’s disagreements about the evidence which prompt questions of probability and risk.
For instance, a gambler at the roulette wheel has seen seven reds in a row and has convinced himself that black is “due”. The probability of black, using the evidence he assumed, is high. Therefore, the risk to him of losing whatever amounts he bets is low.
The operator of the wheel disagrees with the gambler. He reasons that the results of previous spins do not change the causes operating on the ball-wheel combination, and so the probability of black is just under 50% (it’s not 50% because of the green slot or slots). The risk the gambler loses his bet is modest and fixed, to the operator.
Both probabilities and both risks are correct. But most of us would ridicule the gambler, because we recognize the operator has got his facts right, and the gambler doesn’t. The facts or assumptions, the evidence used, all belong to the right hand side of the probability and risk calculation; e.g. Pr(black | assumptions), Risk(bet | assumptions). Once these assumptions are specified, and the proposition to be assessed is agreed upon, the probability and risk both follow deductively.
The facts, or rather assumptions, the gambler uses are just as real to him as the facts used by the operator. But the operator’s match Reality, while the gambler’s do not. The match or mismatch both come in the causes of the wheel’s operation. The operator correctly identified part of the nature of these causes, the gambler has not. The gambler has assumed there exists a mystery cause that somehow restores balance. He “discovered” this cause by perhaps reasoning that he has tracked the wheel a long time and noticed blacks and reds are about equal. Something must be causing this equality!
Something is, but it is not the force he imagines. Imagination can be strong, much stronger than boring demonstrations of fact. The operator can explain, perhaps with the assistance of a mechanic, how the wheel works in nauseating detail, and show the gambler scads of past sequences, but these are just so many words. The gambler believes in his mystery cause, and has seen it operate. He believes. The facts about the wheel are not—they really are not—proof the mystery cause doesn’t exist. The mechanic did not offer proof, and none will ever be forthcoming, for there can be none.
Yet some gamblers learn their error. How? Ideally, they use their mystery-cause model—model is another word for assumptions—and compare it against the mechanical model used by the operator. Gamblers keen to learn see which model does better, they see who really has risked more and less. The repeated sting of losses using the mystery-cause model might be enough to cause him to lose his faith. But only might.
What about coronadoom? Now, I mean, as the virus ebbs. In New York City, the gamblers wear masks. Many more people now wear masks than when the virus was killing people. The fear in the eyes of the masked when they walk by an unmasked person is live and real (I have told you many stories), even when the masked are young and (seemingly) healthy.
We could present the fearful plots showing the attributed deaths have dropped to zero or near zero, and have been at that level for weeks; or we could give them arguments about age and attributed deaths, herd immunity, and the like. But all of this is akin to the roulette operator vainly trying to convince the gambler of his folly.
The fearful believe mysterious forces work against them, forces which they are—barely—holding at bay. The fear itself becomes a mystery force and helps repel the enemy. Just like the gambler, pointing to Reality will not convince the fearful of anything. All we can hope for is that repeated exposure of the fearfuls’ model with Reality will produce enough stings (small as each would be) to make adhering to their model more painful than embracing Reality. Like all things, this will happen gradually, then suddenly.
The lesson is: we are always arguing about causes, and our knowledge of causes. Or, rather, we should be.
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