Random variable ordering

Lexicographic dominance

Lexicographic dominance is a total order between random variables. It is a form of stochastic ordering. It is defined as follows. 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. (Wikipedia).

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Strategyproofness | Ordinal Pareto efficiency | Random variable | Total order | Envy-freeness | Stochastic dominance | Stochastic ordering | Social choice theory | Fair random assignment