[1] It was later generalized by Haris Aziz to handle the case where agents may express indifferences.
Therefore, the procedure should return an allocation that is envy-free for every preference relation that is consistent with the item ranking and with weak additivity.
Note that in a NEF assignment, Alice and George receive the same number of items.
The AL procedure is slightly more complicated, but it guarantees that the contested pile is never larger, and may be smaller than under BT.
For example, suppose there are four items (1, 2, 3, 4) and the preferences of the partners are: The BT procedure gives 1 to Alice and 2 to George, since these are their favorites and they are different.
Both procedures are manipulable: a partner can gain by reporting incorrect preferences.
The original AL procedure crucially relies on the assumption that the item rankings are strict.