A Class of New Methods for Congressional Apportionment

This paper develops a class of new methods for congressional apportionment by building upon and extending the recent work done by M. L. Balinski and H. P. Young. The class, which also includes the Balinski–Young Quota Method, consists of all apportionment methods satisfying two basic criteria (satisfying quota and house monotonicity) articulated by Balinski and Young. The class is defined for both the pure apportionment problem and the apportionment problem with minimum requirements. In the latter case, a new generalization of lower quota is presented, which differs from Balinski and Young’s generalization. Finally, reasons are given for rejecting the Balinski–Young Quota Method and preferring instead one of the new methods in the class.