On Huntington Methods of Apportionment

A (generalized) Huntington method for apportioning representatives among states, or seats among parties, is one which distributes seats one by one by using a rank index that determines how deserving a state, or party, is to receive the next available seat. A characterization of these methods is given by two basic properties; consistency and monotonicity. The arguments used to establish this result are combinatorial in nature and use classical theorems concerning partial orders and their representation by a real-valued function.