ABSTRACT
Suppose, for example, the gain were so huge that a tiny chance of it still had a very high EU. For example, suppose the expected gain were a billion (109) pounds. This is a 0.000000001 (10-9) chance of a quintillion pounds, a quintillion being a million trillion or 1018. He will still prefer the virtual certainty of £2m. Allais asks rhetorically, ‘Who could claim that such a man is irrational? He accepts the first because it gives him a practical certainty of gaining [£2m] and refuses the second because it gives him a practical certainty of being ruined’ (Allais, 532, my translation. We ignore here any complication arising from the diminishing marginal utility of money.)
Reasonable, prudent people ‘begin in effect by fixing a maximum loss which they do not want in any case to exceed, then
C 0.11 chance of £2m EU = D 0.1 chance of £10m EU =
0.89 chance of £0 0.22m 0.9 chance of £0 £1m
they choose by comparing their expected mathematical gain with their chance of ruin, but here it is not a case of mathematical expected gain M of monetary values g, but of mathematical expectation µ of psychological values γ . . .’ (533).
