Mathematics ofApportionment 229 All of these apportionment schemes, except for Hamilton's, are examples of divisor methods. ... An apportionment method satis-fies the Population Property if and only if it is a “generalized” divisor method, where the rounding method may depend on the number of states and the house size. NOT THIS JAMES DEAN WE'RE TALKING ABOUT James Dean (1776-1849) Professor of Astronomy & Mathematics Dartmouth College University of Vermont Historical Significance: Method of Harmonic Means (1832) DEAN VS. WEBSTER What does The question of how the concept of fairness can best be defined, in the context of evaluating an apportionment formula, remains open. The 1870 Apportionment. Pp. If Congress had chosen the method of the harmonic mean, also known as the "Dean Method," Montana would have received a second seat after the 1990 census. 4-13. Officially, Hamilton’s method was in place and the size of the House was agreed to be 292. • Dean’s Method – Cutoff for rounding is (n − 1)n n − 0.5. Consequently, Webster, Dean, and the Huntington-Hill method have never violated quota on any US states dataset so far, and according to some vaguely-described computer experiments by B&Y would be expected to do so only with probability 0.00061, 0.00154, and 0.000286 respectively, which in the case of Webster would be once every 1600 apportionments, i.e. Congress never agreed on an apportionment method, so the U.S. House was not reapportioned until after [7:227. dean: Return apportioned vector according to Dean's Method In jalapic/apportR: Apportionment Tools and Data Description Usage Arguments Value References Further details Examples Each apportionment method discussed in this report has a rational basis, and for each, there is at least one test according to which it is the most equitable. Huntington-Hill (or Huntington, or Hill, or the method of equal proportions) has been used after every Census since 1940. Professor Edelman discusses the background of "one person one vote" in the congressional apportionment context and asserts that because of a mathematical flaw, the Court in U.S. Department of Commerce v. Montana incorrectly permitted a method of congressional apportionment that is not in accordance with "one person one vote." Difference. Difference. Montana . Relative . But the actual apportionment that occurred agreed with Dean’s method, not Hamilton’s method. The absolute and relative differences between the actual average district size and the ideal district size in an apportionment using the Dean Method (Montana has 2 Representatives, and Washington has 8 Representatives) are as follows: Average. From Ideal. 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