Stochastic Dominance

Stochastic dominance is a form of stochastic ordering. The term is used in decision theory and decision analysis to refer to situations where one gamble (a probability distribution over possible outcomes, also known as prospects) can be ranked as superior to another gamble. It is based on preferences regarding outcomes. A preference might be a simple ranking of outcomes from favorite to least favored, or it might also employ a value measure (i.e., a number associated with each outcome that allows comparison of multiples of one outcome with another, such as two instances of winning a dollar vs. one instance of winning two dollars.) Only limited knowledge of preferences is required for determining dominance. Risk aversion is a factor only in second order stochastic dominance.

Stochastic dominance does not give a complete ordering: For some pairs of gambles, neither one stochastically dominates the other, yet they cannot be said to be equal.

A related concept not included under stochastic dominance is deterministic dominance, which occurs when the least preferable outcome of gamble A is more valuable than the most highly preferred outcome of gamble B.