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...ox]], although [[Seat bias|unbiased]] apportionment rules like [[Webster's method]] do so only rarely. ...eats than the upper or lower frame, that allocation (and by extension, the method used to allocate it) is said to be in violation of the quota rule. ...

'''Optimal apportionment''' is an approach to [[Mathematics of apportionment|apportionment]] that is based on [[mathematical optimization]]. In a problem of apportionment, there is a ''resource'' to allocate, denoted by <math>h</math>. For exampl ...

{{Short description|Property of apportionment methods}} ...should not lose a seat while <math>B</math> gains a seat. An apportionment method violating this rule may encounter '''population paradoxes'''. ...

{{Short description|Method of allocating seats in a parliament}} ...then no state (or party) should have fewer seats than it previously had. A method that fails to satisfy house-monotonicity is said to have the '''Alabama par ...

...09-01}}</ref>{{Rp|75}}''' is a property of [[Mathematics of apportionment|apportionment methods]], which are methods of allocating identical items between among ag .... In particular, both [[Highest averages method]]s and [[Largest remainder method]]s are balanced. ...

{{Short description|Metric for fairness of apportionment methods}} ...name=":22">{{Cite journal |last=Ernst |first=Lawrence R. |date=1994 |title=Apportionment Methods for the House of Representatives and the Court Challenges |url=http ...

...irement was first studied in the context of [[Mathematics of apportionment|apportionment]]. In this context, failure to satisfy coherence is called the '''new state == Coherence in apportionment == ...

.... demographic quotas),<ref>{{Cite journal|date=1994-01-01|title=Chapter 15 Apportionment|url=https://www.sciencedirect.com/science/article/abs/pii/S0927050705800969 ...rtionment identifies what properties can be expected from an apportionment method. ...

...Weaker Parties: Majorization |date=2017 |work=Proportional Representation: Apportionment Methods and Their Applications |pages=149–157 |editor-last=Pukelsheim |edit ...quota-proportional methods include the [[expanding approvals rule]], the [[method of equal shares]], and the [[single transferable vote]].<ref name=":12">{{C ...