Question 14.57

image image 27. Explain why the new states paradox (see page 585) cannot occur if a divisor method of apportionment is used. (Would the divisor used in the apportionment after the new state joined the union have to be different from the divisor used before?)

27.

Let be the divisor used to apportion before the new state is added. Let be the population of the new state. The new state should be apportioned , where square brackets indicate the method of rounding that is specified for the particular divisor method in use. This is the formula that would be used for each of the states before and after the new state joined; therefore, none of the original apportionments would change.

Seats Demopublicans Repocrats Greenocrats Greenicans Independents
Priority Seat Priority Seat Priority Seat Priority Seat Priority Seat
1 44,856 1 34944 2 20,004 4 19,002 5 9,804 11
2 22,428 3 17,472 6 10,002 10 9,501 12 4,902
3 14,952 7 11,648 8 6,668 17 6,334 19 3,268
4 11,214 9 8,736 14 5,001 4,751 2,451
5 8,971 13 6,989 16 4,001 3,800 1,961
6 7,476 15 5,824 20 3,334 3,167 1,634
7 6,408 18 4,992 2,858 2,715 1,401
8 5,607 4,368 2,501 2,375 1,226

The Demopublicans get 7 seats, the Repocrats get 6, the Greenocrats and the Greenicans each get 3, and the Independents get 1 seat.