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Bernoulli's hypothesis


A hypothesis, first formulated by D. Bernoulli, that the decision of an individual on whether or not to accept a particular gamble depended on the utility which he attached to the sums of money involved, and not just the sums themselves. For example, consider the following gamble: we toss a coin; if it comes up heads, I pay you £10, if tails, you pay me £9. The probability of getting a head is ½, as is the probability of getting a tail. Hence the 'expected value' to you of the gamble is given by: ½(£10) -½(£9) = £0.50. This has the interpretation that, if we played. this game a large number of times, on average you would end up winning £0.50 per game. Hence we would expect you to accept the gamble and, indeed, be prepared to pay anything up to £0.50 per game for the right to be allowed to play.

However, Bernoulli observed several paradoxes which arose from this view, and it appeared to be refuted by experience - people did reject gambles whose expected values were positive. This could be rationalized in the following way. Suppose the marginal utility of income is diminishing, so that it is quite possible that the gain in utility from winning £10 is smaller than the. loss in utility from losing £9. For example, suppose we could measure these utilities as a gain of 4 units and a loss of 5 units respectively. Then, in deciding whether or not to accept the gamble, our individual would find that the utility he can expect to get from the gamble is negative, i.e. that ½(4) - ½(5) = -½, and he would reject the gamble.

This emphasis on utility values rather than the absolute money values now plays an extremely important role in the economic theory of risk and uncertaninty,- and the Bernoulli hypothesis has turned out to be of fundamental importance.

Reference: The Penguin Dictionary of Economics, 3rd edt.