Population monotonicity

Population monotonicity is a feature of electoral systems. It is often stated as a criterion for party list methods, and by extension, for multi-winner methods in general. The term was first used by Balinski and Young in 1974.

The population monotonicity criterion for a party list method is:

By extension, the population monotonicity criterion for a multi-member system is closely related to the participation criterion

The population paradox is a counter-intuitive result of some procedures for apportionment. When two states have populations increasing at different rates, a small state with rapid growth can lose a legislative seat to a big state with slower growth.

Some of the earlier Congressional apportionment methods, such as the Hamilton method, could exhibit the population paradox. In 1900, Virginia lost a seat to Maine, even though Virginia's population was growing more rapidly. However, every highest averages method, including the current Huntington-Hill method, passes the criterion.