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Jefferson’s method was used to apportion the House after the censuses
of 1790, 1800, 1810, 1820 and 1830.
After the violation of the quota
rule was discovered in 1832, a search began for a better method of
apportionment.
John Quincy Adams, a former President now serving
as a member of the House from Massachusetts, proposed an
apportionment method that is the mirror image of Jefferson’s.
Adams’ method:
Find a modified divisor
d
so that when each state’s modified quota is
rounded upward, the sum of the resulting modified upper quotas is the
exact number of seats to be apportioned.
Example:
Repeat problem 2 with Adams’ method and 26 seats.
Solution:
The standard divisor was
1000
26
000
,
26
=
.
We need
smaller quotas so let’s try dividing by something larger.
Let’s try
1080.
State
Population Quota Upper
quota
Modified
quota
(d
=
1080)
Modified
upper
quota
Modified
quota
(d=
1110)
Mo
up
qu
North
9061
9.061
10
8.389
9
8.163
9
South
7179
7.179
8
6.647
7
6.467
7
East
5259
5.259
6
4.869
5
4.737
5
West
3319
3.319
4
3.073
4
2.990
3
Central
1182
1.182
2
1.094
2
1.064
2
Total
26,000
26
30
27
26
Example:
Use Adams’ method to apportion 250 seats among the
following 6 states:
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View Full DocumentState Population
A
1,646,000
B
6,936,000
C
154,000
D
2,091,000
E
685,000
F
988,000
Solution:
The total population is 12,500,000 and so the standard
divisor is 12,500,000
÷
250 = 50,000.
We need smaller quotas so let’s
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 Spring '08
 Storfer

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