Von Neumann and Mongenstern develop a theory of utility (Utility Theory) in which they show that, yes, utility grows logarithmically with the wealth at stake, both positively and negatively (loss of wealth, as already indicated by Bernoulli two centuries earlier), but that we also have the hope of large gains, for which we are willing to pay more than we should, and the aversion to the risk, even minimal, of losing what we possess, for which we are also willing to pay more than we should. Lotteries make money on the first flaw (of System 2 according to Kahneman and Tversky’s nomenclature), while insurance and pension systems make money on the second.
