Population Number of
District (in thousands) Fraction of State Quota Representatives
A 42 10.219 2.55 3
B 81 19.708 4.93 5
C 288 70.073 17.52 17The next time the census is taken, the population of District A has in-
creased by 1,000, District C has increased by 6,000, while the population
of District B is unchanged. The table now becomes
Population Number of
District (in thousands) Fraction of State Quota Representatives
A 43 10.2871 2.57 2
B 81 19.3780 4.84 5
C 294 70.3349 17.60 18The population of District A has increased by 2.38 percent, whereas the
population of District C has increased by 2.08 percent. District A is grow-
ing more rapidly than District C, but has actually lost a representative. It
would certainly seem fairer that if District C is to gain a representative, it
should do so at the expense of District B, which isn’t growing at all, and,
in fact, could even be shrinking and still receive the same number of
seats under the Hamilton method.
The New States Paradox
The Hamilton method failed one last time in 1907, when Oklahoma joined
the Union. Prior to Oklahoma’s entrance into the Union, the House of Rep-
resentatives had 386 seats. On a proportion basis, Oklahoma was entitled to
5 seats, so the House was expanded to include 386 5 391 representatives.
However, when the seats were recalculated, it was discovered that Maine
had gained a seat (from 3 to 4), and New York had lost a seat (from 38 to 37).
They’re suffering from similar problems in the following example,
where a representative house has twenty-nine seats.
District Population (in thousands) Quota Number of Representatives
A 61 3.60 3
B 70 4.13 4
C 265 15.65 16
D 95 5.61 6232 How Math Explains the World
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