AAAS - Mathematics of Congressional Apportionment David...

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Unformatted text preview: Mathematics of Congressional Apportionment David Housman Goshen College The Constitutional Basis “Representatives and direct Taxes shall be apportioned among the several States which may be included within this Union, according to their respective Numbers . . . . The actual Enumeration shall be made within three years after the first meeting of the Congress of the United States, and within every subsequent Term of ten Years, in such manner as they shall by Law direct.” article I, section 2 What is the Problem? CA UT population of CA quota house size population of USA 33,930,798 435 52.447 281,424,177 population of UT quota house size population of USA 2,236,714 435 3.457 281,424,177 = × = × = = × = × = CA UT apportionment 53 apportionment 3 = = The above figures are from the 2000 census, and the official apportionment is A Small Example State Population Quota Apportionment i p i q i a i 1 9,598 47.99 2 5,868 29.34 3 2,664 13.32 4 1,870 9.35 Total 20,000 100.00 • Rounding does not work. • The extra seat should go to the state with the • smallest population p i • largest remainder r i = q i- q i • largest relative remainder r i / p i Hamilton’s Method Give to each state the whole number contained in its quota, and then assign remaining seats to states with the largest quota remainders. State Population Quota Apportionment i p i q i a i 1 9,598 47.99 47 + 1 = 48 2 5,868 29.34 29 + 0 = 29 3 2,664 13.32 13 + 0 = 13 4 1,870 9.35 9 + 1 = 10 Total 20,000 100.00 100 Jefferson’s Method Choose an ideal district size. Give each state its whole number of seats. If the house size is fixed, the ideal district size must be chosen so that the seats assigned matches the house size. State Population Districts Apportionment i p i p i / 195.7 a i 1 9,598 49.04 49 2 5,868 29.98 29 3 2,664 13.61 13 4 1,870 9.56 9 Total 20,000 100 State Population Districts Apportionment i p i p i / 200 a i 1 9,598 47.99 47 2 5,868 29.34 29 3 2,664 13.32 13 4 1,870 9.35 9 Total 20,000 98 Webster’s Method Choose an ideal district size. Give each state its rounded number of seats. If the house size is...
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AAAS - Mathematics of Congressional Apportionment David...

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