Population monotonicity: Difference between revisions
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'''Population monotonicity''' is a feature of electoral systems. It is often stated as a criterion for [[ |
'''Population monotonicity''' is a feature of electoral systems. It is often stated as a criterion for [[party list]] methods, and by extension, for [[multi-member system|multi-winner 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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The |
The population monotonicity criterion for a [[party list]] method is: |
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{{Definition| If the number of voters increases |
{{Definition| If the number of voters increases then the party which the new voter endorsed cannot lose a seat.}} |
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By extension, the population monotonicity criterion for a [[multi-member system]] is closely related to the [[participation criterion]] |
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The '''population paradox''' is a counter-intuitive result of some procedures for apportionment. When two states have populations increasing at different rates, a small state with rapid growth can lose a legislative seat to a big state with slower growth. |
The '''population paradox''' is a counter-intuitive result of some procedures for apportionment. When two states have populations increasing at different rates, a small state with rapid growth can lose a legislative seat to a big state with slower growth. |
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Some of the earlier Congressional apportionment methods, such as the [[Hamilton method]], could exhibit the population paradox. In 1900, Virginia lost a seat to Maine, even though Virginia's population was growing more rapidly. However, |
Some of the earlier Congressional apportionment methods, such as the [[Hamilton method]], could exhibit the population paradox. In 1900, Virginia lost a seat to Maine, even though Virginia's population was growing more rapidly. However, every [[highest averages method]], including the current Huntington-Hill method, passes the criterion.<ref name=Smith>{{cite web |url=http://rangevoting.org/Apportion.html |title=Apportionment and rounding schemes |last=Smith |first=Warren D.}}</ref> |
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==See also== |
==See also== |
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* [[Participation criterion]] |
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* [[Balinski–Young theorem]] |
* [[Balinski–Young theorem]] |
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* [[Highest averages method]] |
* [[Highest averages method]] |
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* [[House monotonicity criterion]] |
* [[House monotonicity criterion]] |
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==References== |
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Latest revision as of 11:33, 30 April 2022
Population monotonicity is a feature of electoral systems. It is often stated as a criterion for party list methods, and by extension, for multi-winner methods in general. The term was first used by Balinski and Young in 1974.[1]
The population monotonicity criterion for a party list method is:
If the number of voters increases then the party which the new voter endorsed cannot lose a seat.
By extension, the population monotonicity criterion for a multi-member system is closely related to the participation criterion
The population paradox is a counter-intuitive result of some procedures for apportionment. When two states have populations increasing at different rates, a small state with rapid growth can lose a legislative seat to a big state with slower growth.
Some of the earlier Congressional apportionment methods, such as the Hamilton method, could exhibit the population paradox. In 1900, Virginia lost a seat to Maine, even though Virginia's population was growing more rapidly. However, every highest averages method, including the current Huntington-Hill method, passes the criterion.[2]
See also
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.
- ↑ Smith, Warren D. "Apportionment and rounding schemes".