State Fraction of Population Quota (37 Fraction)
A .14 5.18
B .23 8.51
C .45 16.65
D .18 6.66Each quota is a mixed number; an integer plus a fractional part, the
fractional part being expressed as a decimal. Each state is initially as-
signed the integer part of its quota, as indicated by the following table.State Quota Initial Assignment Remaining Fraction
A 5.18 5 .18
B 8.51 8 .51
C 16.65 16 .65
D 6.66 6 .66The total initial assignment of representatives is 5 8 16 6 35,
which is 2 representatives short of the desired total of 37. These two rep-
resentatives are assigned to the states in decreasing order of the leftover
fraction. D has the largest leftover fraction (.66), and so gets the first of
the two remaining representatives. C has the next largest leftover fraction
(.65), and is awarded the second remaining representative. A and B come
up short in this process. The final tally is shown in the following table.
State Percentage of Population Number of Representatives
A .14 5
B .23 8
C .45 17
D .18 7In 1880, C. W. Seaton, the chief clerk of the U.S. Census Office, discov-
ered a curious anomaly in the Hamilton method. He decided to compute
the number of representatives each state would receive if the House had
anywhere from 275 to 350 seats. In so doing, he discovered that Alabama
would have received 8 representatives if the House had 299 representa-
tives, but if the size of the House increased to 300, Alabama would receive
only 7 representatives! Thus the Alabama paradox.
The Smoke- Filled Rooms 229