House monotonicity criterion: Difference between revisions
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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
{{Definition| If the number of seats increases with fixed populations,
That is, a state must never lose a seat from the number of total seats increasing. When used as a [[party list]] system, no party can lose a seat in this way, either. The [[Alabama paradox]] is an example of a house monotonicity failure.
By extension, the house monotonicity criterion for a [[
{{Definition|
That is, increasing the number of winners should never evict anyone from the [[winner set]] who is already in it.
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.
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* [[Balinski–Young theorem]]
* [[Population monotonicity]]
== References ==
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