The Hillelite rulings are usually less strict and more pragmatic, and the order is almost always the same: the Shammaites and then the Hillelites. Perhaps it reflects the fact that the Hillelites got the last words because they won by surviving after 70 CE. When Jerusalem was destroyed, the Shammaites were almost all dead, killed during the destruction. So the Hillelites were victors by surviving. Or maybe that order reflects the fact that the Shammaites were superior originally, that is, in the