Balinski–Young theorem: Difference between revisions

{{cite book |title=Fair Representation: Meeting the Ideal of One Man, One Vote |edition=2nd |last=Balinski |first=M |author2=Young HP|year=2001 |publisher=Brookings Institution Press |isbn=0-8157-0111-X }}

</ref> The theorem shows that any possible method used to allocate the remaining fraction will necessarily fail to always follow quota. More precisely, their theorem states that there is no apportionment system that has the following 3 properties <ref name=Stein2008>Stein JD. How Math Explains the World: A Guide to the Power of Numbers, from Car Repair to Modern Physics. Smithsonian. Apr 22, 2008. {{ISBN|9780061241765}}</ref> (as the example we take the division of seats between parties in a system of [[proportional representation]]):

* It has [[House monotonicity criterion | House monotonicity]]: If the total number of seats is increased, no party's number of seats decreases.

 

== Specific Systems==