Microeconomics: Stochastic dominance

What on earth is THAT!?

Allow me to briefly explain. Let us assume two lotteries (a lottery is a probability distribution over certain payoffs, or outcomes). Let us call them lottery A and B.

If ALL individuals with a non-decreasing utility function unanimously prefer lottery A to B, we say that lottery A stochastically dominates lottery B.

If 999,999 individuals (say, in a population of 1,000,000 individuals) prefer lottery A to lottery B, but ONE does not, then lottery A DOES NOT stochastically dominate lottery B. As you can seen, stochastic dominance is a pretty strong notion.

In a case for ANY type of non-decreasing utility function where A stochastically dominates B, we say that A first-order stochastically dominates B. In a case where we consider only non-decreasing concave utility functions where A stochastically dominates B, we say that A second-order stochastically dominates B. Note that second-order stochastic dominance implies first-order stochastic dominance, as concave, non-decreasing utility functions are a subset of all non-decreasing utility functions.

On a separate note... sometimes I wonder... 'stochastic domination' sounds cooler than 'stochastic dominance'! Vad tror du? (What do you think?)