Editing Apportionment paradox (section)

{{Short description|Pathological behavior by an apportionment rule}}
An '''apportionment paradox''' is a situation where an [[Apportionment (politics)|apportionment]]—a rule for dividing discrete objects according to some [[proportionality (mathematics)|proportional relationship]]—produces results that violate notions of [[common sense]] or [[justice|fairness]].

Certain quantities, like milk, can be divided in any proportion whatsoever; others, such as horses, cannot—only whole numbers will do. In the latter case, there is an inherent tension between the desire to obey the rule of proportion as closely as possible and the constraint restricting the size of each portion to discrete values.

Several paradoxes related to apportionment and [[fair division]] have been identified. In some cases, simple adjustments to an apportionment methodology can resolve observed paradoxes. However, as shown by the Balinski–Young theorem, it is not always possible to provide a perfectly fair resolution that satisfies all competing fairness criteria.<ref name=Stein2008>{{cite book |last = Stein |first = James D. |title = How Math Explains the World: A Guide to the Power of Numbers, from Car Repair to Modern Physics |location = New York |publisher = Smithsonian Books |year = 2008 |isbn = 9780061241765 }}</ref>{{rp|227–235}}