The term **Stochastic dominance** is used in decision theory to refer to situations where one lottery (a probability distribution over outcomes) can be ranked as superior to another, with only limited knowledge of preferences. Decision theory is an interdisciplinary area of study, related to and of interest to practitioners in mathematics, statistics, economics, philosophy, management and psychology. ...
The simplest case, **statewise dominance** arises when one prospect gives a better outcome than another in every possible state of nature (more precisely, at least as good an outcome in every state, with strict inequality in at least one state). For example, if a dollar is added to every prize in a lottery, the new lottery statewise dominates the old one. Anyone who prefers more to less (in the standard terminology, anyone who has monotonic preferences) will always prefer a statewise dominant lottery. In mathematics, functions between ordered sets are monotonic (or monotone) if they preserve the given order. ...
The canonical case of stochastic dominance, referred to as **first-order stochastic dominance** arises when for any outcome *x*, the dominant distribution gives a higher probability of receiving an outcome equal to or better than *x* than the dominated distribution. The other commonly used case of stochastic dominance is **second-order stochastic dominance**. All risk-averse expected-utility maximizers prefer a second-order stochastically dominant lottery to a dominated lottery. The same is true for non-expected utility maximizers with concave local utility functions. Higher orders of stochastic dominance have also been analyzed, as have generalizations of the dual relationship between stochastic dominance orderings and classes of preference functions. |