Lexicographic_dominance
Lexicographic dominance
Statistical property
Lexicographic dominance is a total order between random variables. It is a form of stochastic ordering. It is defined as follows.[1]: 8 Random variable A has lexicographic dominance over random variable B (denoted ) if one of the following holds:
- A has a higher probability than B of receiving the best outcome.
- A and B have an equal probability of receiving the best outcome, but A has a higher probability of receiving the 2nd-best outcome.
- A and B have an equal probability of receiving the best and 2nd-best outcomes, but A has a higher probability of receiving the 3rd-best outcome.
In other words: let k be the first index for which the probability of receiving the k-th best outcome is different for A and B. Then this probability should be higher for A.