Answer
The Alabama paradox occurs. Initially, with a total of 24 seats to be allocated, State A was allocated 4 seats. After the total number of seats to be allocated increased to 25, State A was allocated only 3 seats.
Work Step by Step
We can find the standard divisor.
$standard~divisor = \frac{total ~population}{number~of~ seats}$
$standard~divisor = \frac{3760}{24}$
$standard~divisor = 156.7$
We can find each state's standard quota. The standard quota of each state is the state's population divided by the standard divisor.
State A:
$standard ~quota = \frac{population}{standard~divisor}$
$standard~quota = \frac{530}{156.7}$
$standard~quota = 3.38$
State B:
$standard ~quota = \frac{population}{standard~divisor}$
$standard~quota = \frac{990}{156.7}$
$standard~quota = 6.32$
State C:
$standard ~quota = \frac{population}{standard~divisor}$
$standard~quota = \frac{2240}{156.7}$
$standard~quota = 14.29$
Hamilton's method is an apportionment method that involves rounding each standard quota down to the nearest whole number. Surplus seats are given, one at a time, to the states with the largest decimal parts in their standard quotas until there are no more surplus seats.
Initially, each state is apportioned its lower quota.
State A is apportioned 3 seats.
State B is apportioned 6 seats.
State C is apportioned 14 seats.
The total number of seats which have been apportioned is 3 + 6 + 14 = 23 seats
Since there is a total of 24 seats, there is one surplus seat. One more seat is given to State A because it has the largest decimal part (0.38) in its standard quota.
Using Hamilton's method, each state is apportioned the following number of seats:
State A is apportioned 3 + 1 = 4 seats.
State B is apportioned 6 seats.
State C is apportioned 14 seats.
We can find the standard divisor when the total number of seats increases from 24 to 25.
$standard~divisor = \frac{total ~population}{number~of~ seats}$
$standard~divisor = \frac{3760}{25}$
$standard~divisor = 150.4$
We can find each state's standard quota. The standard quota of each state is the state's population divided by the standard divisor.
State A:
$standard ~quota = \frac{population}{standard~divisor}$
$standard~quota = \frac{530}{150.4}$
$standard~quota = 3.52$
State B:
$standard ~quota = \frac{population}{standard~divisor}$
$standard~quota = \frac{990}{150.4}$
$standard~quota = 6.58$
State C:
$standard ~quota = \frac{population}{standard~divisor}$
$standard~quota = \frac{2240}{150.4}$
$standard~quota = 14.89$
Hamilton's method is an apportionment method that involves rounding each standard quota down to the nearest whole number. Surplus seats are given, one at a time, to the states with the largest decimal parts in their standard quotas until there are no more surplus seats.
Initially, each state is apportioned its lower quota.
State A is apportioned 3 seats.
State B is apportioned 6 seats.
State C is apportioned 14 seats.
The total number of seats which have been apportioned is 3 + 6 + 14 = 23 seats
Since there is a total of 25 seats, there are two surplus seats. The first seat is given to State C because it has the largest decimal part (0.89) in its standard quota. The second seat is given to State B because it has the second largest decimal part (0.58) in its standard quota.
Using Hamilton's method, each state is apportioned the following number of seats:
State A is apportioned 3 seats.
State B is apportioned 6 + 1 = 7 seats.
State C is apportioned 14 + 1 = 15 seats.
We can see that the Alabama paradox occurs. Initially, with a total number of 24 seats, State A was allocated 4 seats. After the total number of seats increased to 25, State A was allocated only 3 seats. Therefore, the Alabama paradox occurs.
