House monotonicity criterion: Difference between revisions
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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. The [[Alabama paradox]] is an example of a house monotonicity failure. |
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By extension, the house monotonicity criterion for a multi-member method is: |
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> |
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{{Definition| |
{{Definition|No candidate should be harmed by an increase in the number of seats to be filled, with no change to the profile.}} |
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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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Revision as of 16:40, 4 February 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. The Alabama paradox is an example of a house monotonicity failure.
By extension, the house monotonicity criterion for a multi-member method is:[2]
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[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
- ↑ 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.
- ↑ Woodall, D. (1994). "Properties of preferential election ruiles". Voting matters (3): 8–15.
- ↑ Markus Schulze (2011-03-14). "Free Riding and Vote Management under Proportional Representation by the Single Transferable Vote" (PDF). p. 42.