Before revision:  This answers an open question of AG18 . We find that when DA is OSP, priorities are either acyclic Erg02 , or contain an extremely limited cyclic pattern where all priority lists are identical except for exactly two.
After revision:  This answers an open question of AG18 . We find that when DA is OSP, priorities are either acyclic (Ergin, 2002), a restrictive condition which allows priorities to only differ on only two agents at a time , or contain an extremely limited cyclic pattern where all priority lists are identical except for exactly two.