Editing Expected utility hypothesis (section)

=== Bernoulli's formulation ===
[[Nicolaus I Bernoulli|Nicolaus Bernoulli]] described the [[St. Petersburg paradox]] (involving infinite expected values) in 1713, prompting two Swiss mathematicians to develop expected utility theory as a solution. Bernoulli's paper was the first formalization of [[marginal utility]], which has broad application in economics in addition to expected utility theory. He used this concept to formalize the idea that the same amount of additional money was less useful to an already wealthy person than it would be to a poor person. The theory can also more accurately describe more realistic scenarios (where expected values are finite) than expected value alone. He proposed that a nonlinear function of the utility of an outcome should be used instead of the [[expected value]] of an outcome, accounting for [[risk aversion]], where the [[risk premium]] is higher for low-probability events than the difference between the payout level of a particular outcome and its expected value. Bernoulli further proposed that it was not the goal of the gambler to maximize his expected gain but to maximize the logarithm of his gain instead.{{citation needed|date=August 2023}}

Daniel Bernoulli drew attention to psychological and behavioral components behind the individual's [[decision-making process]] and proposed that the utility of wealth has a [[diminishing marginal utility]]. For example, an extra dollar or an additional good is perceived as less valuable as someone gets wealthier. In other words, desirability related to a financial gain depends on the gain itself and the person's wealth. Bernoulli suggested that people maximize "moral expectation" rather than expected monetary value. Bernoulli made a clear distinction between expected value and expected utility. Instead of using the weighted outcomes, he used the weighted utility multiplied by probabilities. He proved that the utility function used in real life is finite, even when its expected value is infinite.<ref name=":2" />