A note on ex-ante stable lotteries

We study ex-ante priority respecting (ex-ante stable) lotteries in the context of object allocation under thick priorities. We show that ex-ante stability as a fairness condition is very demanding: Only few agent-object pairs have a positive probability of being matched in an ex-ante stable assignment. We interpret our result as an impossibility result. With ex-ante stability, one cannot go much beyond randomly breaking ties and implementing a (deterministically) stable matching with respect to the broken ties.