What is first order stochastic dominance?

First order stochastic dominance is a criterion used in decision making theory to compare probability distributions. It states that one distribution dominates another if the cumulative distribution function of the first distribution is always greater than or equal to that of the second distribution for all possible outcomes. This means that the first distribution is always at least as likely to produce a better outcome than the second distribution, regardless of the decision maker's preferences.

Mathematically, if F(x) and G(x) are the cumulative distribution functions of two random variables X and Y, respectively, then F(x) ≥ G(x) for all values of x, and we say that X dominates Y in the first order stochastic sense.

First order stochastic dominance is an important concept in economics, finance, and risk management, where it is often used to compare different investment options. It is a relatively simple criterion to apply and can provide useful insights into the decision-making process. However, it is important to note that first order stochastic dominance is a weak criterion, in that it does not take into account the decision maker's preferences for different outcomes. For this reason, it is often used in conjunction with other decision criteria, such as second order stochastic dominance or expected utility theory.