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The '''House monotonicity criterion''' is a criterion for apportionment/party list methods, and by extension, for multi-member 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 house monotonicity criterion for an apportionment method is:

{{Definition| If the number of seats increases with fixed populations, no state delegation decreases.}}

That is, a state must never lose a seat from the number of total seats increasing. The [[Alabama paradox]] is an example of a house monotonicity failure.

By extension, the house monotonicity criterion for a multi-member method is:<ref name="Woodall 1994 Properties">{{cite journal | last=Woodall |first=D. |title=Properties of preferential election ruiles | journal=Voting matters | issue=3 | pages=8–15 | year=1994 | url=http://www.votingmatters.org.uk/ISSUE3/P5.HTM}}</ref>

{{Definition|No candidate should be harmed by an increase in the number of seats to be filled, with no change to the profile.}}

House monotone multi-member methods are sometimes called proportional orderings or proportional rankings<ref>{{cite web|url=http://9mail-de.spdns.de/m-schulze/schulze2.pdf|title=Free Riding and Vote Management under Proportional Representation by the Single Transferable Vote|date=2011-03-14|author=Markus Schulze|page=42}}</ref>, and James Green-Armytage's [[Proportional Ordering]] is such a method. Sequential methods without deletion steps, such as [[sequential Ebert]] and [[Sequential Phragmen|sequential Phragmén]], are also house monotone.

==Related==

* [[Balinski–Young theorem]]

== References ==

[[Category:Voting system criteria]]