Brady on Keynes’ Theoretical Approach
ME Brady J. M. Keynes’s Theoretical Approach to Decision-making Under Conditions of Risk and Uncertainty Brit. J. Phil. Sci. 44 (1993), 357-3 76
Well before the economic crisis of 2007/8 Brady was pointing out that most other economists were ignoring Keynes’ Treatise on Probability and were even claiming that Keynes offered no mathematical alternative to conventional (numeric) probability. He describes a formula of Keynes’ for discounting utility to take account of both risk aversion and a limited weight of evidence. He then shows how this can help explain both Ellsberg’s and Popper’s ‘paradoxes’, some insurance examples, and a behavioural ‘anomaly’ of Kahneman & Tversky.
“… Keynes’s conventional coefficient of risk and weight offers a truly modern up-to-date decision rule.”
Brady treats Keynes’ formula as a ‘rule’, without identifying the associated assumptions or theory, other than by encouraging the reader to consult Keynes’ Treatise. The rule thus appears both more ad-hoc and more general than it really is. But Brady does remind us that it is possible to say something useful about some domains (e.g. insurance) using mathematics that goes well beyond the conventional case, and the approach can be generalized if we – as Keynes did – adapt the formula to the actual cases at hand.
One way to consider the treatment of uncertainty is as a strategy in which one seeks to avoid a loss in the long run which, with hind-sight, could have been avoided. Various rules will then arise according to the nature of the problem situation. Keynes’ formula applies when the uncertainties are statistical. It thus applies to ‘normal’ insurance.