Shackle’s Decision, Order and Time
G.L.S. Shackle Decision Order and Time 2nd Edition, CUP 1969
Shackle was an economist who sought to develop the ideas of Keynes, among others. His work, written in ‘plain English’, seems to me very strained and obscure. But an interpretation along the lines of Keynes’ Treatise seems to help.
Preface (to the first edition)
…the rival possible outcomes for which a man will imagine for an available act of his own cannot be listed from a knowledge, however complete, of what is and what has been. … the use of a distributional uncertainty variable, that is, probability, becomes in principal inappropriate … .
Shackle reserves the term decision for a decisive selection, as against something that is predetermined according to some rule, such as in utility maximization. He aims to replace probability with a new concept, surprise. Surprises arise, for example, when someone-else makes a decision.
Part I Time
IV Insulated Dynamic Schemes
A dynamic scheme that is unaffected by decisions is said to be insulated. Thus dynamic schemes are only insulated in what we might call ‘the short-run’. An action-scheme, like a policy or strategy, allows for selections by others, and thus has actions that are contingent on the actions of others and hence for their action-schemes. Dynamic schemes are insulated as long as the action schemes are not changed. Thus, for example, in game-theory a fixed game would be an insulated dynamic scheme. A game-of-games would not be insulated.
V Three Critics
[T]he decision-maker uses knowledge, logic and tense and anxious judgement in composing his imaginative picture of what might lie beyond each gate that each rival choice of act might open.
VI Time and Decision in Sum
The set of rival hypothetical outcomes of each available action is not prescribed like those of a game with completely stated rules.
Part II Uncertainty
VII Uncertainty as probability
Here Shackle takes a largely psychological perspective, rather than building on part I.
When an individual elects to marry or not to marry, to become a surgeon instead of an engineer; when a statesman decides to challenge rather than appease an aggressive enemy … the entire subsequent career of an individual or of a nation is swung onto one rather than another of two wholly different channels. … there can be no going back to the state of affairs which prevailed while the choice was still open. … such experiments (sic) are self-destructive.
… In abolishing the experimental character of many acts, and virtually depriving them in effect of any uncertainty as to their relevant outcomes, statistical probability yet leaves a vast field of action untouched. Isolated and, above all, self-destructive experiments, numerous enough and of crucial and dominating importance when they arise, are inherently untouchable by it.
IX Uncertainty as possibility
The argument is largely psychological. Surprise is not linked to part I, or even the preface. Shackle rejects distributionality (i.e., summing to 1) but accepts the view that components of uncertainty should be totally ordered, having ‘degrees’ that are similar to conventional degrees of belief. In effect, he simply argues for unbelief, rather than belief. Surprise seems related to Keynes’ notion of likelihood, but Shackle only wets our appetite.
X Potential surprise axiomatized
The axioms are for the most part met by 1-likelihood, with the exception of axiom (7), which implies a qualitative interpretation. This may be motivated by part I. A draw-back of this axiomatization is that it deals with surprise separately from classical probability, whereas an overarching theory would be desirable.
Part IV Expectation of change of own expectation
Can a decision-maker’s viewpoint expectations, bearing on some outcome the truth about which will be known at the later of two future dates, include the idea that at the earlier of these dates he will entertain a different expectation from the one he entertains at his viewpoint? Can he expect a change of his own expectations?
Shackle gives a motivation for his axiom (7). He draws a distinction between the notion of ‘A and B’, as in Bayes’ rule, and ‘A then B’.
We claim three things for our rule:
first, that … it is …less remote from reality [than Bayes’ rule];
secondly, that it has greater simplicity than any other rule; and
thirdly, that this simplicity is not bought at too high a sacrifice of realism.
Thus Shackle does not intend his ‘axiom’ to be taken too literally (or mathematically), only as ‘indicative’.
A man cannot without logical contradiction say to himself: ‘I should be greatly surprised if event F occurred . But there is an event E which, if it were to occur intermediately, would make me feel that event F would be very little surprising; and moreover, I shall not be at all surprised if event E does occur.’
Knight, like Shackle, consider conventional probability theory inadequate. Shackle’s ‘insulated dynamic schemes’ have some points of similarity with Whitehead‘s epochs, each of which has it own ‘rules’ or character. This ‘goes with’ Keynes‘ notion of uncertainty, whose nature depends on the nature of the epoch, which is further developed by Russell. It is also worth noting that game theory is not as restricted as Shackle supposes. Both hold that a situation with fixed rules is a special case.
Shackle built on Keynes’ General Theory, but seems to have overlooked his mathematical treatment of uncertainty, which is unfortunate. While Shackle uses some mathematical language and formulae, this book might most easily be taken as a reasoned criticism of more mainstream views, and a challenge to construct an alternative. But some of his descriptions improve upon the more mathematical works.
If we take Keynes’ view, we may consider the current and anticipated epochs, associating uncertainty with each. In the short-run, this could be conventional subjective probability, or objective probability with some factors unknown. The transitions between epochs may be either due to self-reinforcing chance (whose possibility Shackle neglects) or Shackle’s decisions. In some cases decisions might be modelled conventionally as games. In others we may have no reasonable model. In a particular case we would then have something like Shackle’s strange axiom (7), but dependent on the case at hand. Shackle’s ‘surprise’ would then be ‘unlikelihood’ – the converse of likelihood.
With this interpretation, the accessible bits of this book seem consistent with Keynes and to emphasise much the same points, but perhaps more accessible.