I [Taleb] spent a long time believing in the centrality of probability in life and advocating that we should express everything in terms of degrees of credence, with unitary probabilities as a special case for total certainties, and null for total implausibility. Critical thinking, knowledge, beliefs, everything needed to be probabilized. Until I came to realize, twelve years ago, that I was wrong in this notion that the calculus of probability could be a guide to life and help society. Indeed, it is only in very rare circumstances that probability (by itself) is a guide to decision making . It is a clumsy academic construction, extremely artificial, and nonobservable. Probability is backed out of decisions; it is not a construct to be handled in a standalone way in real-life decision-making. It has caused harm in many fields. . . .
We can easily see that when it comes to small odds, decision making no longer depends on the probability alone. It is the pair probability times payoff (or a series of payoffs), the expectation, that matters. . . .
What causes severe mistakes is that, outside the special cases of casinos and lotteries, you almost never face a single probability with a single (and known) payoff. You may face, say, a 5% probability of an earthquake of magnitude 3 or higher, a 2% probability of one of 4 or higher, etc. The same with wars: you have a risk of different levels of damage, each with a different probability. "What is the probability of war?" is a meaningless question for risk assessment. . . .
The point is mathematically simple but does not register easily. I've enjoyed giving math students the following quiz (to be answered intuitively, on the spot). In a Gaussian world, the probability of exceeding one standard deviations is ~16%. What are the odds of exceeding it under a distribution of fatter tails (with same mean and variance)? The right answer: lower, not higher — the number of deviations drops, but the few that take place matter more. It was entertaining to see that most of the graduate students get it wrong. . . .
Another complication is that just as probability and payoff are inseparable, so one cannot extract another complicated component, utility, from the decision-making equation. . . .
Read my previous posts on Nassim Taleb: