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The problem of apportionment is explained together with an account of the methods used by the United States Congress beginning with the first decennial apportionment of 1792. Fairness and historical precedent dictate that several properties must be satisfied by any method which may be deemed acceptable. It is shown that the method presently used violates one of these and that a new procedure, the quota method, is the unique method satisfying the essential properties.
Balinski et al. (1975) studied this question.