George L. S. Shackle, “Probability and Uncertainty” (1949/1955)

Shackle’s essay is a theoretical critique of the assumption that probability, understood as frequency-ratio probability, can guide all rational choice. He begins from Keith West’s story of Kwong Hui, a Chinese sentry tempted by rebellion, to show that some decisions cannot be converted into actuarial calculations. The relevant outcome for Kwong Hui is not one member of a class of repeated trials, but a fate that absorbs the whole future of the chooser.

Having one’s head cut off is, for the person concerned, rather final.

The essay does not deny the usefulness of probability. Shackle grants that in suitably uniform, repeatable circumstances—coin tosses, dice throws, or other experiments that can be run many times—frequency ratios can give genuine knowledge about an aggregate series. But this knowledge applies to the series as a whole, not necessarily to the single occasion whose consequence is decisive for one person. His argument turns on two conditions: first, that the underlying performances be sufficiently uniform and numerous; second, that the contemplated experiment be divisible into many similar instances whose gains and losses can be pooled.

The second condition is the crucial one. Many economic and practical decisions are not divisible in this sense. Insurance, repeated trading, and large portfolios may transform some risks into manageable aggregates, but a person choosing a career, undertaking a decisive investment, or committing political treachery cannot always treat the outcome as one item in a compensating series. Shackle calls such choices “crucial” experiments.

By a crucial experiment I mean one where the person concerned cannot exclude from his mind the possibility that the very act of performing the experiment may destroy for ever the circumstances in which it was performed.

This definition gives the essay its distinctive economic importance. A crucial experiment may change not only external conditions but also the chooser’s own situation: age, wealth, information, confidence, reputation, and imaginative outlook. A business venture undertaken once cannot simply be repeated by the same person under the same conditions after success or ruin. Likewise, a career decision made in youth cannot be rerun with youth restored. The act helps create the world in which later acts would occur.

For that reason, Shackle rejects the transfer of long-run frequency reasoning to singular, history-making choices. A frequency ratio may describe a class of trials, but it does not by itself answer the question faced by the person for whom this one trial is decisive. The point is not that the future is mysterious in every respect, but that the relevant object of judgment is often not a repeatable experiment.

For a non-divisible non-seriable experiment the concept of frequency-ratios is wholly irrelevant.

Shackle then asks what remains when actuarial reasoning fails. His answer is not irrationalism, but a theory of choice under uncertainty as imaginative appraisal. The decision-maker entertains rival hypotheses about what might follow from each act. These hypotheses differ not by additive numerical probabilities summing to one, but by their power to stimulate hope or fear and by their degree of “potential surprise.” Doubt, in this account, is not equivalent to measurable probability; it is an aspect of how vividly and plausibly a possible future can be entertained.

To feel enjoyment or distress by anticipation is to feel it by imagination.

The later argument contrasts an “integrative” solution, which would somehow combine all imagined gains and losses, with a “focus-values” solution. Shackle favors the latter: since mutually exclusive possibilities cannot all be treated as jointly realized, the mind focuses on especially significant imagined outcomes—a focus-gain and a focus-loss attached to each course of action. Choice is then shaped by the comparative pull of these representative hopes and fears, not by expected value in the frequency sense.

The essay belongs to the Knight-Keynes-Shackle tradition of distinguishing calculable risk from uncertainty. Its central claim is that economics must not disguise crucial, non-repeatable decisions as lotteries with known frequencies. In many of the choices that matter most, the future is not a stable urn from which outcomes are drawn, but an imaginative field of rival possibilities created in part by the very act of choosing.