House monotonicity criterion: Difference between revisions
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{{merge from|Alabama paradox|discuss=Talk:Alabama paradox}}
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>
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{{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. 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 [[multi-member
{{Definition|No candidate should be harmed by an increase in the number of seats to be filled, with no change to the profile.}}
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.▼
▲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
==Criterion incompatibility==
{{See also|Left, Center, Right}}
Methods that are house monotone and pass the [[Droop proportionality criterion]] all fail the [[Condorcet criterion]]. A method may pass any two of these criteria, but not all three at once.
==Related==
* [[Balinski–Young theorem]]
* [[Population monotonicity]]
== References ==
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