Proportional Consistency of Apportionment Methods
摘要
We analyze a little-known property of apportionment methods that captures how allocations scale with the size of the house: specifically, if, for a fixed population distribution, the house size and allocation can be scaled down within the set of integers, then the apportionment should be correspondingly scaled down. Balinski and Young [1] include this property among the minimal requirements for a “reasonable” apportionment method. We argue that this property is better understood as a consistency requirement since quota-based apportionments that are “less proportional” meet this requirement while others that are “more proportional” do not. We also show that the family of so-called quotatone methods based on stationary divisors (including the quota method [2]) do not satisfy this property.