Judgment under Uncertainty: Heuristics and Biases

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   A question that looks impossible becomes estimable once you break it into steps you can approximate; but if every step must happen, their probabilities multiply, and the total is lower than the weakest step.

   Judgment under Uncertainty: Heuristics and Biases · 1974

   If every step must happen, you multiply the probabilities, and the result is lower than the weakest step.

   Tetlock and Gardner hold up Enrico Fermi as a model: he enjoyed ballparking answers to questions such as ‘how many extraterrestrial civilizations exist in the universe?’. The trick is not genius but decomposition: break the question into pieces you can approximate, separate what you know from what you do not, and put your assumptions in plain view. The errors of the parts tend to offset each other, and a written assumption can be corrected. With probabilities, decomposition exposes a trap. A plan succeeds only if every step happens, so the probabilities of the steps, each conditional on the ones before, multiply. Tversky and Kahneman (1974, p. 1129) show that people overestimate conjunctive events and underestimate disjunctive ones: participants preferred to bet on drawing a red marble seven times in a row from a bag that was 90% red (probability 0.48) rather than on a simple 0.50 event. The anchor is the probability of a single step, and the adjustment away from it is insufficient. The rule to check at any time: the probability that A and B both happen cannot exceed the smaller of the two, and the probability that at least one happens cannot be below the larger. The second half matters for risks: a system with many components fails if any one of them gives way. The premortem in the olivLaw engine asks the model for five failure modes with probabilities, but checks neither of these bounds.

   “Biases in the evaluation of compound events are particularly significant in the context of planning. The successful completion of an undertaking, such as the development of a new product, typically has a conjunctive character: for the undertaking to succeed, each of a series of events must occur. Even when each of these events is very likely, the overall probability of success can be quite low if the number of events is large.”

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