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 solves an open problem of Ashlagi and Gonczarowski, 2018. 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.