Balinski–Young theorem: Difference between revisions
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* It has [[Population monotonicity]]: If party A gets more votes and party B gets fewer votes, no seat will be transferred from A to B.
== Specific
Methods may have a subset of these properties, but can't have all of them:
* A method may follow quota and be free of the Alabama paradox. Balinski and Young constructed a method that does so, although it is not in common political use.<ref>{{cite journal |last=Balinski |first=M |author2=Young HP |year=1974 |title=A new method for congressional apportionment |journal=Proceedings of the National Academy of Sciences |volume=71 |issue=11 |pages=4602–4606 |doi=10.1073/pnas.71.11.4602|pmc=433936 |pmid=16592200}}</ref>
* A method may be free of both the Alabama paradox and the population paradox. These methods are [[Highest averages method|divisor methods]],<ref name=Smith>{{cite web |url=http://rangevoting.org/Apportion.html |title=Apportionment and rounding schemes |last=Smith |first=WD}}</ref> and [[W:Huntington-Hill method|Huntington-Hill]], the method currently used to apportion House of Representatives seats, is one of them. However, these methods will necessarily fail
* No method may always follow quota and be free of the population paradox.<ref name=Smith/>
* [[Largest remainder method | Largest remainder methods]] obey Quota Rules but have neither of the other two criteria. The [[Hamilton method]] of apportionment is actually a largest-remainder method which is specifically defined as using the Hare Quota
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