Population monotonicity (PM) is a principle of consistency in allocation problems.
[1]: 46–51 [2] The term "population monotonicity" is used in an unrelated meaning in the context of apportionment of seats in the congress among states.
In the fair cake-cutting problem, classic allocation rules such as divide and choose are not PM.
[5] In the fair item allocation problem, the Nash-optimal rule is no longer PM.
Moreover, round-robin can be adapted to yield picking sequences appropriate for agents with different entitlements.