Adam Smith on lotteries: an interpretation and formal restatement

The paper concerns a neglected aspect of the Wealth of Nations (with the notable exception of D. Levy 1999), dealing directly with decision under risk. In a few pages from book I, chapter 10, Adam Smith explicitly named “lotteries” various objects of choice (possible occupations, or investment opportunities, for instance) and provided an analysis which standard expected utility glasses would hardly fit. Taking this into account allows a better understanding of the part played by typical characters like the “projector” or the “sober man”, in such matters as Smith’s conception of entrepreneurship or of the credit market. The use of some modern concepts in decision analysis (inverse stochastic dominance, rank dependent utility, prudence toward risk), is a means to show the existence, in Smith’s work, of an original theory from decision under risk, where his analysis of lotteries in the Wealth of Nations is consistent with statements from his moral philosophy on asymmetric sensitivity to gains and losses and to the regulating part played by the impartial spectator.