Chapter 4 Handout 1 Solutions
Solution to
Problem#1:
The standard divisor is the total population divided by the number of seats which equals
13.9 million people divided by 25 seats which equals .56 million people/seat.
The standard divisor is the ratio of population to seats.
Here for every .56 million people there is 1 seat.
Notice that, using Hamilton’s apportionment, there are no lower or upper quota violations.
state
population
in millions
standard
quota
lower
quota
upper
quota
fractiona
l part
ranking
Hamilton
apportionmen
t
MA
6.3
11.33
11
12
.33
11
CT
3.4
6.12
6
7
.12
6
ME
1.4
2.52
2
3
.52
Second
3
NH
1.2
2.16
2
3
.16
2
RI
1.0
1.80
1
2
.8
First
2
VT
0.6
1.08
1
2
.08
1
Total
13.9
25
23
29
25
Solution to Problem#2:
Notice that, using Hamilton’s apportionment, there are no lower or upper quota violations.
state
populatio
n
standard
quota
lower
quota
fractional
part
ranking
Hamilton
apportionment
MA
7.0
15.24
15
.24
15
CT
3.8
8.27
8
.27
8
ME
2.0
4.35
4
.35
Secon
d
5
NH
1.8
3.92
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 Spring '07
 Berkowitz
 Math, Division, Multiplication, Ratio, Fraction

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