@toby-pereira said in Variable house sizes:
Do you think a method not violating quota is a matter of principle or simply that it looks better if it doesn't? Because interestingly enough, while Hamilton doesn't violate quota, Webster is simply Hamilton but without the IIB failures. For two parties they are identical.
I somewhat agree, in that I think those ballots are irrelevant for splitting the A+B between A and B: the relative apportionments of parties A or B shouldn't depend on how many votes another party gets.
On the other hand, I think such a ballot (one that supports C, but not A or B) is actually so irrelevant that, not only should this ballot not affect an "idealized" apportionment (i.e. the number of seats each party would get, if we didn't have to deal with rounding); it actually shouldn't even affect the actual relative apportionment.
Say we declare the relative apportionment of A and B shouldn't depend at all on a ballot that supports C (as the vote ratio of A relative to B has not changed). Sometimes, though, adding a ballot that supports C will cause C to gain a seat. The only way to uphold our restriction, that the seat ratio of A to B should not depend on the addition of an irrelevant ballot (one disapproving both A and B) is to make sure that extra seat for C doesn't come from either A or B.
I actually find this strong monotonicity property (impossible to satisfy in a fixed-size committee) much more pleasing/important than quota. If forced to deal with a fixed committee size, I'll accept violations of quota. I much prefer Webster to Hamilton, but Hamilton+Webster (choosing the house size so both methods agree) results in a stronger population monotonicity property than either one alone.