The table below gives the populations of four districts A, B, C, and D, among which a total of 20 seats are to be apportioned. \begin{tabular}{lcccc} \hline District & A & B & C & D \\ Population & 544,000 & 183,000 & 229,000 & 98,000 \\ \hline \end{tabular} How many seats does district A receive using Jefferson's method? A. 11 B. 10 C. 9 D. 12
Solution
Step 1 ：Calculate the standard divisor. The total population is \(544,000 + 183,000 + 229,000 + 98,000 = 1,054,000\). The total number of seats is 20. So, the standard divisor is \(1,054,000 / 20 = 52,700\).
Step 2 ：Calculate the standard quotas. For district A, the standard quota is \(544,000 / 52,700 = 10.32\).
Step 3 ：Apply Jefferson's method. In Jefferson's method, we round down the standard quotas. So, district A would initially receive 10 seats.
Step 4 ：Adjust the divisor. If we round down the standard quotas for all districts, we would end up with fewer than 20 seats. So, we need to adjust the divisor downward to increase the quotas. This is done through trial and error. If we adjust the divisor to 50,000, the quota for district A becomes \(544,000 / 50,000 = 10.88\).
Step 5 ：Round down the quotas. After adjusting the divisor, we round down the quotas again. So, district A would receive 10 seats.
Step 6 ：\(\boxed{10}\) is the final answer.
