Population monotonicity

From electowiki

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.[1]

The population monotonicity criterion for a party list method is:

If the number of voters increases then the party which the new voter endorsed cannot lose a seat.

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.[2]

See also


  1. Balinski, M. L.; Young, H. P. (1974-11-01). "A New Method for Congressional Apportionment". Proceedings of the National Academy of Sciences. Proceedings of the National Academy of Sciences. 71 (11): 4602–4606. doi:10.1073/pnas.71.11.4602. ISSN 0027-8424.
  2. Smith, Warren D. "Apportionment and rounding schemes".