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''' 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 a [[Party list]] method is:
The house monotonicity criterion for an apportionment method is:


{{Definition| If the number of seats increases with fixed populations, then no party can have its number of seats decrease.}}
{{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.
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 System]] is:<ref name="Woodall 1994 Properties">{{cite journal | last=Woodall |first=D. |title=Properties of preferential election rules | journal=Voting matters | issue=3 | pages=8–15 | year=1994 | url=http://www.votingmatters.org.uk/ISSUE3/P5.HTM}}</ref>
By extension, the house monotonicity criterion for a [[multi-member system]] is:<ref name="Woodall 1994 Properties">{{cite journal | last=Woodall |first=D. |title=Properties of preferential election rules | journal=Voting matters | issue=3 | pages=8–15 | year=1994 | url=http://www.votingmatters.org.uk/ISSUE3/P5.HTM}}</ref>


{{Definition|If only the seat count is increase then the [[Winner set]] must include all prior winners }}
{{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 without deletion steps, such as [[sequential Ebert]] and [[Sequential Phragmen|sequential Phragmén]], are also house monotone.
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* [[Balinski–Young theorem]]
* [[Balinski–Young theorem]]
* [[Population monotonicity]]
* [[Population monotonicity]]

== References ==
== References ==



Revision as of 20:12, 23 March 2020

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.[1]

The house monotonicity criterion for an apportionment method is:

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 system is:[2]

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[3], and James Green-Armytage's Proportional Ordering is such a method. Sequential methods without deletion steps, such as sequential Ebert and sequential Phragmén, are also house monotone.

Related

References

  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. Woodall, D. (1994). "Properties of preferential election rules". Voting matters (3): 8–15.
  3. Markus Schulze (2011-03-14). "Free Riding and Vote Management under Proportional Representation by the Single Transferable Vote" (PDF). p. 42.