Random Matching and assignment under dichotomous preferences

We consider bilateral matching problems where each person views those on the other side of the market as either acceptable or unacceptable: an acceptable mate is preferred to remaining single, and the latter to an unacceptable mate all acceptable mates are welfare-wise identical. Using randomization, many efficient and fair matching methods define strategyproof revelation mechanisms. Randomly selecting a priority ordering of the participants gives a simple example. Equalizing as much as possible the probability of getting an acceptable mate accross all participants stands out for its normative and incentives properties: the profile of probabilities is Lorenz dominant, and the revelation mechanism is groupstrategyproof for each side of the market. Our results apply to the random assignment problem as well.