A small county has populations in three districts as shown below. They are to apportion 15 seats on the county council using the Hill-Huntington method. Find the apportionment for each district. $$\begin{array} { l c }
\text { District } & \text { Population } \
\text { Parkview } & 43,000 \
\text { Hillside } & 32,800 \
\text { Riverdale } & 24,200
\end{array}$$
A) 7, 5, 3
B) 6, 6, 3
C) 6, 5, 4
D) 7, 4, 4

Question

A small county has populations in three districts as shown below. They are to apportion 15 seats on the county council using the Hill-Huntington method. Find the apportionment for each district. $$\begin{array} { l c } 
\text { District } & \text { Population } \
\text { Parkview } & 43,000 \
\text { Hillside } & 32,800 \
\text { Riverdale } & 24,200
\end{array}$$
A) 7, 5, 3
B) 6, 6, 3
C) 6, 5, 4
D) 7, 4, 4

Quizplus · Accepted Answer

Step 1: Calculate the standard divisor (SD)
$	ext{SD}=\frac{	ext{County Population}}{	ext{Number of Seats}}=\frac{99,000}{15}=6,600$
Step 2: Calculate the adjusted quotas (AQ)
AQ = $\frac{	ext{District Population}}{	ext{SD}}$
Parkview AQ = $\frac{43,000}{6,600}\approx6.52$
Hillside AQ = $\frac{32,800}{6,600}\approx4.97$
Riverdale AQ = $\frac{24,200}{6,600}\approx3.66$
Step 3: Calculate the initial apportionment (IA)
IA = $\sum$AQ
IA = 6+4+3 = 13
Step 4: Calculate the remainder seats (RS)
RS = $	ext{Number of Seats}-	ext{IA}$
RS = 15-13 = 2
Step 5: Identify the districts with the largest remainder (LR)
Parkview LR = 0.52
Hillside LR = 0.03
Riverdale LR = 0.34
Parkview has the largest remainder. Therefore, it gets the first remaining seat.
Step 6: Recalculate adjusted quotas for Parkview with one more seat
AQ = $\frac{	ext{Parkview Population}}{	ext{SD} + 1} = \frac{43,000}{6,600 + 1} \approx 6.39$
Hillside AQ = $\frac{32,800}{6,600}\approx4.97$
Riverdale AQ = $\frac{24,200}{6,600}\approx3.66$
Step 7: Calculate the new apportionment
New apportionment = IA + 1
New apportionment = 6+5+4 = 15
The apportionment for each district is therefore 6, 5, 4. So, the best choice is C.

A Small County Has Populations in Three Districts as Shown