2. What is Apportionment?
Distributing something
proportionally to different
groups
Apportion house
representatives to the US
states based on state
population
We figure out population of
states and country from
census (residents, not
including green card
holders)
3. Hamilton Method
1. Compute the standard divisor,
d = total population/total number of
seats
2. Compute the standard quota for each
state, Q = state’s population/d
3. Round each state’s standard quota Q
down to the nearest integer. Each state will
get at least this many seats, but must get at
least one.
4. Give any additional seats one at a time
(until no seats are left) to the states with
the largest fractional parts of the their
standard quotas.
Used: (1850 – 1900)
4. Hamilton Method in Action (Alabama + D.C.)
Alabama
1. Standard divisor,
d= total pop/house seats
d=320,820,975/435
d= 737,519.48
2. Alabama Standard Quota,
Q=state pop/d
Q=4,802,982/737,519.48
Q= 6.51
3. Round Q down to nearest integer
(must be at least 1)
New Q = 6
D.C.
1. Total pop/house seats
d = 737,519.48
2. D.C. Standard Quota
Q = state pop/d
Q = 601,723 / 737,519.48
Q = 0.82
3. Round Q down to nearest integer
(must be at least 1)
New Q = 0 (must be at least 1
though!)
New Q = 1
6. Jefferson Method
Steps:
1. Compute md, the modified divisor.
2. Compute mQ, the modified quota
for each state.
mQ = state’s population/md
3. Round each state’s modified quota mQ
down to the nearest integer.
4. Give each state this integer number of
seats.Used: (1790 – 1840)
7. Jefferson Method in Action (Alabama + D.C.)
Alabama
1. Modified divisor (a number I
made up)
md= 739,000
2. Modified Quota,
mQ=state pop/md
mQ=4,802,982/739,000
mQ= 6.499
3. Round mQ down to nearest
integer
New Q = 6
D.C.
1. Total pop/house seats
md= 739,000
2. D.C. Modified Quota
mQ = state pop/md
mQ = 601,723 / 739,000
mQ = 0.82
3. Round Q down to nearest
integer
New Q = 0
Uh oh! Jefferson Method doesn’t
work too well
9. Adams Method
Steps:
1. Compute md, the modified
divisor.
2. Compute mQ, the modified quota
for each state.
3. Round each state’s modified quota
mQ up to the nearest integer.
4. Give each state this integer number
of seats.
10. Webster Method
Steps:
1. Compute md, the modified divisor.
2. Compute mQ, the modified quota for
each state
mQ = state’s population/md
3. Round each state’s modified quota mQ
up to the nearest integer if its fractional part
is greater than or equal to .5 and down to
the nearest integer if its fractional part is
less than .5.
4. Give each state this integer number of
seats.
(1840 – 1850)
(1910 – 1940 )
11. Hill-Huntington Method
Steps:
1. Compute md, the modified divisor.
2. Compute mQ, the modified quota for each
state.
3. Take two integers, one is mQ rounded up, the
other is mQ rounded down. Take geometric mean
(square root of mQ1*mQ2). If mQ is less than
geometric mean, round down. If mQ is greater than
it, round up.
4. Give each state this integer number of seats.
(1940 – present)
12. Hill-Huntington Method in Action (Alabama and
D.C.)
Alabama
1. Modified divisor (a number I made up)
md= 745,000
2. Modified Quota,
mQ=state pop/md
mQ=4,802,982/745,000
mQ= 6.446
3. Round mQ down and up to nearest
integer
New Q = 6/7
4. Geometric mean = sqrt(6*7) = 6.48
mQ < Geometric mean, so we round
down
5. Reps = 6
D.C.
1. Total pop/house seats
md= 745,000
2. Modified Quota
mQ = state pop/md
mQ = 601,723 / 745,000
mQ = 0.808
3. Round Q down and up to nearest
integer
New Q = 0/1
4. Geometric mean = sqrt(0*1) = 0
mQ > Geometric mean, so we round up
5. Reps = 1
