A small county has populations in three districts as shown below. They are to apportion 15 seats on the county council using the Webster 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 Webster 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

Using the Webster method, we first find the standard divisor: 
$$	ext{Standard Divisor} = \frac{	ext{Total Population}}{	ext{Number of Seats}} = \frac{99,000}{15} = 6,600$$
Next, we find the priority values for each district by using the following formula: 
$$	ext{Priority Value} = \frac{	ext{Population}}{	ext{Standard Divisor}}$$
Thus, the priority values for each district are: 
$$\begin{array}{c|c}
	ext{District} & 	ext{Priority Value} \ \hline
	ext{Parkview} & \frac{43,000}{6,600} \approx 6.52 \
	ext{Hillside} & \frac{32,800}{6,600} \approx 4.97 \
	ext{Riverdale} & \frac{24,200}{6,600} \approx 3.67 \
\end{array}$$
We then assign seats one at a time to each district according to the priority values. After each allocation of a seat, we update the priority values and continue until all 15 seats are allocated. The apportionment is:

- District Parkview: $\lfloor 6.52 floor + 1 = 7$ seats
- District Hillside: $\lfloor 4.97 floor + 1 = 5$ seats
- District Riverdale: $\lfloor 3.67 floor + 1 = 4$ seats

Therefore, the answer is C) 6, 5, 4.

A Small County Has Populations in Three Districts as Shown