Chapter 4, Problem 21E

The small nation of Fireland is divided into four counties: Arcadia, Belarmine, Crowley, and Dandia. Fireland uses Jefferson's method to apportion the 100 seats in the Chamber of Deputies among the four counties. Table 4-31 shows the population.

Table 4-31

County	Arcadia	Belarmine	Crowley	Dandia
Population	4, 500, 000	4, 900, 000	3, 900, 000	6, 700, 000

a. Find the standard divisor and the standard quotas for each county.

b. Determine how many seats would be apportioned if each county was given its lower quota.

c. Determine how many seats would be apportioned if the divisor $d=197,000$ is used to compute the modified quotas and then all of them are rounded down.

d. Determine how many seats would be apportioned if the divisor $d=195,000$ is used to compute the modified quotas and then all of them are rounded down.

e. Determine how many seats would be apportioned if the divisor $d=197,800$ is used to compute the modified quotas and then all of them are rounded down.

f. Determine how many seats would be apportioned if the divisor $d=196,000$ is used to compute the modified quotas and then all of them are rounded down.

g. Without doing any additional computations, find three different divisors that would work under Jefferson's method.