A family of Hamilton type methods for congressional apportionments

Several principles have been proposed for determining whether the apportionment of seats of a legislative house by a given method is fair. In this work a certain family of methods that satisfy the ‘fair share’ criterion is introduced and it is shown that such methods also satisfy other criteria like the ‘near fair share’ and the ‘partial population monotonicity’. The family includes the traditional Hamilton’s method which is the only one in such a family that satisfies a certain type of ‘independence’.