Huntington-Hill Method
Method of Equal Proportions
Joseph A. Hill, Chief statistician,
Bureau of the Census
Edward V. Huntington, Professor of
Mathematics, Harvard
Some History
• Developed around 1911
• Endorsed by a National Academy of
Sciences Panel in 1929
• Signed into law as our apportionment
method in 1941 when the House size was
set at 435.
Two Questions to Answer
• Why was the Huntington-Hill method
chosen as our apportionment method?
• How does it work?
We will answer the second question first.
(To make our life easier, we will abbreviate
the method as HH!)
Divisor methods and Means
• The HH method is a divisor method. The
difference between it and other divisor
methods is how the quotient for each state
is rounded.
• To understand this rounding method, we
take a side trip and talk about three
different types of means and how they are
used to round in 3 different divisor
methods.
Arithmetic Mean
The arithmetic mean(AM) of two numbers is
their usual ‘average’:
AM(12,13) = (12 + 13)/2 = 12.5
Webster’s method uses this number as the
cutoff for rounding (round down if the
quotient is less than this number.)
Geometric Mean
The geometric mean(GM) of two numbers is
the square root of their product:
GM(12,13) = √(12∙13) = 12.49
Huntington-Hill uses this number as the
cutoff for rounding (rounding down if the
quotient is less than this number.)
Harmonic Mean
The harmonic mean(HM) of two numbers is
twice the product of the two numbers
divided by their sum:
HM(12, 13) = 2∙12∙13/(12 + 13) = 12.48
Dean’s Method uses this number as the
cutoff for rounding (rounding down if the
quotient is less than this number.)
How do the means compare?
• Take four number pairs (4 and 5, 6 and 7,
8 and 9, 10 and 11) and calculate each of
the three means for that pair. Then
compare the sizes of the means and write
down your results (GM<HM<AM, say).
• What do you notice? Test your conjecture
with another pair like 37 and 38.
An example
Do HH and Dean for a divisor of 270
School
Population
East
1500
West
1000
North
9000
South
6000
Central
200