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