Population monotonicity: Difference between revisions

'''Population monotonicity''' is a feature of electoral systems. It is often stated as a criterion for [[Partyparty list]] methods, and by extension, for [[Multimulti-Membermember Systems]]system|multi-winner methods]] in general. The term was first used by Balinski and Young in 1974.<ref name="Balinski Young pp. 4602–4606">{{cite journal | last=Balinski | first=M. L. | last2=Young | first2=H. P. | title=A New Method for Congressional Apportionment | journal=Proceedings of the National Academy of Sciences | publisher=Proceedings of the National Academy of Sciences | volume=71 | issue=11 | date=1974-11-01 | issn=0027-8424 | doi=10.1073/pnas.71.11.4602 | pages=4602–4606}}</ref>

The Populationpopulation monotonicity criterion for a [[Partyparty list]] method is:

By extension, the population monotonicity criterion for a [[Multimulti-Membermember Systemsystem]] is closely related to the [[Participationparticipation criterion]]

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, any type ofevery [[Highesthighest averages method]], such asincluding the current Huntington-Hill method, dopasses the notcriterion.<ref name=Smith>{{cite web |url=http://rangevoting.org/Apportion.html |title=Apportionment and rounding schemes |last=Smith |first=WDWarren D.}}</ref>