this is a helpful article but there is a minor problem with this exposition gamble a has first order stochastic dominance over gamble b if for any good outcome x a gives at least as high a probability of receiving at least x as does b and for some x a gives a higher probability of receiving at least x in notation form p a ge x ge p b ge x for all x and for some x p a ge x p b ge x my capitalisation of good the notation form does not capture the notion of a good outcome x it quantifies over all x good or otherwise would the problem be fixed simply by deleting good in the initial characterisation