Suppose an extra representative will be added to the current total of 15 representatives.

Use the apportionment criterion to decide who should get an additional representative. Justify your answer.

Subdivision A has 560 residents and 6 representatives in the City Hall; whereas, Subdivision B has 765 residents and 9 representatives.


Give the extra representative to Subdivision A because this option results in the smallest relative unfairness. (WOULD THIS BE THE ANSWER)?


Give the extra representative to Subdivision B because this option results in the largest relative unfairness.


Give the extra representative to Subdivision B because this option results in the smallest relative unfairness.


Give the extra representative to Subdivision A because this option results in the largest relative unfairness.

Yes.

To determine who should get the additional representative using the apportionment criterion, we need to consider the relative unfairness of each option.

The relative unfairness in apportionment can be measured using various methods, such as the absolute method or the rounding method. However, in this case, we have not been provided with the specific method to be used, so we will consider the relative unfairness based on the rounding method.

To calculate the relative unfairness, we can compare the ideally rounded representatives for each subdivision with the actual number of representatives. The ideally rounded representative for each subdivision can be calculated by dividing the number of residents in each subdivision by the current total number of representatives (15), and then rounding the result to the nearest whole number.

Using this approach, we can calculate the ideally rounded representatives as follows:

Subdivision A: 560 residents / 15 representatives ≈ 37.33 ≈ 37 ideally rounded representatives
Subdivision B: 765 residents / 15 representatives ≈ 51 ideally rounded representatives

Now, let's evaluate the relative unfairness based on these calculations:

Option 1: Give the extra representative to Subdivision A
In this case, the number of representatives for Subdivision A would increase from 6 to 7, while Subdivision B would remain at 9. The relative unfairness can be calculated as the difference between the actual number of representatives and the ideally rounded number of representatives:

Subdivision A: 7 - 37 = -30
Subdivision B: 9 - 51 = -42

Option 2: Give the extra representative to Subdivision B
In this case, the number of representatives for Subdivision A would remain at 6, while Subdivision B would increase from 9 to 10. The relative unfairness can be calculated as:

Subdivision A: 6 - 37 = -31
Subdivision B: 10 - 51 = -41

Based on these calculations, we can see that both options result in negative relative unfairness values, indicating a deviation from the ideally rounded representatives. However, the option with the smallest negative relative unfairness is to give the extra representative to Subdivision A. Therefore, the correct answer would be:

Give the extra representative to Subdivision A because this option results in the smallest relative unfairness.