Criteria for a "Good" Apportionment System

As we have seen, many different methods have been proposed and used in the U.S. (Hamilton, Jefferson, Webster, Dean, and Huntington-Hill). These methods can sometimes produce strange results and paradoxes.

Quota Rule: A state's apportionment should be either the floor or the ceiling of its ideal quota obtained by dividing its population by the standard divisor s.

Neutrality: Switching the populations of two states results in the switch of their apportionments.

All the methods we have seen satisfy neutrality, but is there a method that satisfies the quota rule and does not have paradoxes?

Balinski-Young Theorem: It is impossible for a neutral apportionment system to satisfy the quota rule and be free of the population paradox.

Balinski and Young argued that the Webster method is the best but we still use the Huntington-Hill method.