My War on the Misuse of Probability

In the preceding post I say that “the problem with history is that the future isn’t part of it.” That is subtle criticism of the too-frequent practice of attributing a probability to the occurrence of a future event — especially a unique event, such as a war here or a terrorist attack there.

A probability is a statement about a very large number of like events, each of which has an unpredictable (random) outcome. Probability, properly understood, says nothing about the outcome of an individual event. It certainly says nothing about what will happen next.

A fair coin comes up heads with a probability of 0.5, and comes up tails with the same probability. But those aren’t statements about the outcome of the next coin toss. No, they’re statements about the approximate frequencies of the occurrence of heads and tails in a large number of tosses. The next coin toss will eventuate in heads or tails, but not 0.5 heads and 0.5 tails (except in the rare and unpredictable case of a coin landing on edge and staying there).

There’s a vast gap between routine processes of the kind to which probabilities attach — coin tosses, for example — and the complexities of human activity. Human activity is too complex and dependent on intentions and willful actions to be characterized (properly) by statements about the probability of this or that action.

It is fatuous to say, for example, that a war on the scale of World War II is improbable because such a war has occurred only once in human history. By that reasoning, one could have said confidently in 1938 that a war on the scale of World War II could never occur because there had been no such war in human history.

(Inspired by Bryan Caplan’s fatuous post, “So Far.”)