Hamilton's Apportionment Method is a way of distributing resources (in this case, computers) among groups (states) based on their population. The general steps for using Hamilton's method are as follows:

1. Calculate Standard Divisor: This is done by dividing the total population by the total number of items to apportion (in this case, computers).

   $\text{Standard Divisor} = \frac{\text{Total Population}}{\text{Total Computers}}$

2. Calculate Standard Quotas: Each state's population is divided by the Standard Divisor to get the standard quota.

   $\text{Quota for each state} = \frac{\text{State Population}}{\text{Standard Divisor}}$

3. Initial Apportionment: Each state is initially assigned the integer part of its quota.

4. Distribute Remaining Items: After the initial apportionment, there may be leftover items. These are distributed one by one to the states with the largest fractional parts of their quotas, until all items are apportioned.

Let's go step-by-step and calculate the answers for both Mississippi and New York based on the table.

Step 1: Calculate the Standard Divisor

The total population is:

$\text{Total Population} = 59700 + 98400 + 45800 + 67300 = 271200$

There are 278 computers to distribute, so the standard divisor is:

$\text{Standard Divisor} = \frac{271200}{278} \approx 975.18$

Step 2: Calculate Standard Quotas

Now, we'll calculate the quota for each state by dividing its population by the standard divisor:

• Mississippi: $\frac{59700}{975.18} \approx 61.24$
• New York: $\frac{98400}{975.18} \approx 100.91$
• Nevada: $\frac{45800}{975.18} \approx 46.98$
• Illinois: $\frac{67300}{975.18} \approx 69.03$

Step 3: Initial Apportionment

Take the integer part of each quota:

• Mississippi: 61
• New York: 100
• Nevada: 46
• Illinois: 69

This gives a total of:

$61 + 100 + 46 + 69 = 276$

So, we have apportioned 276 computers, leaving 2 computers still to be distributed.

Step 4: Distribute Remaining Computers

Now, we distribute the 2 remaining computers based on the fractional parts of the quotas:

• Mississippi: 0.24
• New York: 0.91
• Nevada: 0.98
• Illinois: 0.03

We give one computer each to Nevada (0.98) and New York (0.91), the two states with the largest fractional parts.

Final Apportionment:

• Mississippi: 61
• New York: 101
• Nevada: 47
• Illinois: 69

Answers:

• For Question 17 (Mississippi): B. 61 Computers
• For Question 18 (New York): D. 101 Computers

Would you like further details on Hamilton's method or have any questions?

Here are 5 related questions for further practice:

1. How would the results change if the total population were slightly different?
2. Can Hamilton's method ever result in ties for fractional parts when distributing remaining items?
3. What would happen if we had fewer computers than the integer parts of the quotas?
4. How does Hamilton’s Apportionment differ from Jefferson's Method?
5. Can Hamilton's Apportionment method be used for negative allocations?

Tip: Hamilton's method ensures fairness by first assigning based on whole quotas and then distributing remainders based on fractional parts, making it particularly useful for large-scale apportionment scenarios.