George Lennox Sharman Shackle, “On the Meaning and Measure of Uncertainty: II” (1953)

Shackle’s essay develops a theory of decision under uncertainty for cases where action is singular, consequential, and not assimilable to repeated gambling trials. Its central target is the use of mathematical expectation in entrepreneurial and investment choice. The problem is not simply that probabilities are hard to estimate, but that the form of the decision is different: the investor does not buy a divisible share in a large statistical series, but commits to one course whose future will be one realized history among many imagined possibilities.

Shackle begins from the relation between an imagined outcome and the mind that contemplates it. A possible result has both a value and a degree of credibility or disbelief attached to it. The first element is the gain or loss that would follow if the hypothesis were true.

One of these is the face-value of the hypothesis, that is, some measure of what the decision-maker would gain from adopting the particular course of action, if the hypothesis were to turn out true.

The second element is the “potential surprise” attached to the hypothesis. Shackle’s inquiry asks how these two dimensions can jointly guide conduct. In ordinary probability theory, the answer would be additive expectation: multiply each outcome by its probability and sum the products. Shackle argues that this procedure is justified only where the experiment is divisible or seriable, so that a set of outcomes can be meaningfully possessed as a statistical aggregate. A single business decision lacks that structure.

When the course of action is a non-divisible non-seriable experiment, such an additive procedure loses entirely the relevance it has for a divisible experiment, and has only one claim to fall back on: that of being a compromise.

This distinction lets Shackle separate the logic of games from the logic of economic life. Games of chance are artificially closed worlds: all relevant possibilities are specified by the rules, and unknown influences are excluded. Real investment, by contrast, is exposed to novelty, ignorance, and unenumerated conditions. The future is not merely a draw from a known urn; it is partly constituted by circumstances that cannot be listed in advance.

It is because in the text-book examples of drawings from an urn, and in the games of chance, factors whose existence and nature are unknown are excluded by the rules of the game, that these examples and games are irrelevant to reality.

Shackle’s constructive alternative is a theory of imaginative appraisal. Agents do not survey a complete probability distribution. They form hypotheses about possible outcomes, reject some as too far-fetched, and retain a range of possibilities that are not positively probable in a numerical sense but are not unbelievable. Knowledge therefore works less by assigning precise weights than by ruling out what cannot seriously be entertained.

To say this is simply to say again in different words that men’s knowledge and insight do not usually enable them to specify narrowly what is positively probable, but only to discountenance what is implausible and far-fetched.

Within the remaining field of plausible possibilities, the decision-maker is especially moved by two poles: the most alluring gain he can plausibly hope for and the most serious loss he must plausibly fear. Shackle’s “focus-values” replace the expected value of an entire distribution. A project is appraised through its focus-gain and focus-loss, each combining face-value with potential surprise. The mind is not stimulated equally by all possible outcomes; it is arrested by those extreme but still credible possibilities that define hope and anxiety.

The essay then formalizes this appraisal by translating focus-points with differing potential surprise into standardized equivalents with zero surprise but equal psychological stimulus. A project can thereby be located by a standardized focus-gain and focus-loss. These coordinates enter an indifference map for the enterpriser: a larger feared loss must be offset by a larger hoped-for gain, though temperaments differ in how they treat the possibility of ruin. This framework allows Shackle to reinterpret investment scale and the principle of increasing risk without relying on objective probability.

The result is a distinctive theory of uncertainty as disciplined subjectivity. Shackle does not deny rational choice; he denies that rationality under ignorance must take the form of probability-weighted averaging. In non-repetitive economic action, uncertainty is measured by the limits of plausible imagination: by what the agent can hope for without self-deception and fear without dismissing as fantasy.