A county has three districts with the populations shown below. The 11 seats on the county council are to be apportioned using the Jefferson method. Find the apportionment for each district. $$\begin{array} { c c }
\text { District } & \text { Population } \
\text { A } & 43,000 \
\text { B } & 32,800 \
\text { C } & 24,200
\end{array}$$

Question

A county has three districts with the populations shown below. The 11 seats on the county council are to be apportioned using the Jefferson method. Find the apportionment for each district. $$\begin{array} { c c } 
\text { District } & \text { Population } \
\text { A } & 43,000 \
\text { B } & 32,800 \
\text { C } & 24,200
\end{array}$$

Quizplus · Accepted Answer

Step 1: Calculate the standard divisor = Total population/Total seats = 100,000/11 = 9,090.909
Step 2: Calculate the quota for each district by dividing their population by the standard divisor:
- District A quota = 43,000/9,090.909 = 4.725
- District B quota = 32,800/9,090.909 = 3.604
- District C quota = 24,200/9,090.909 = 2.659
Step 3: Assign each district the whole number part of its quota. District A gets 4 seats, district B gets 3 seats, and district C gets 2 seats.
Step 4: Calculate the remainders for each district:
- District A remainder = 0.725
- District B remainder = 0.604
- District C remainder = 0.659
Step 5: Order the districts by their remainders in descending order, and assign them one additional seat each until all seats are assigned. In this case, district A has the largest remainder, so it gets the first additional seat. Its new quota becomes 5.450, and its remainder becomes 0.540. District B has the next largest remainder, so it gets the second additional seat. Its new quota becomes 4.338, and its remainder becomes 0.338. District C gets the last additional seat. Its new quota becomes 3.008, and its remainder becomes 0.008.
Therefore, the final apportionment is:
- District A: 5 seats
- District B: 4 seats
- District C: 2 seats