Other Divisor Methods
Adams Method
This method rounds the quota up, when Jefferson rounds down. It favors smaller states.
The Process: •
Find the standard divisor, s, by dividing total population/total seats
Determine each states quota, Q, by dividing the state's population/standard divisor
Round the quota to the next highest integer, finding the ceiling of the quota.
Find the total number of seats that the intial Adams Method produces. If It's the intended amount, great! You're done.
If not, the denominator (in the intital calculation, s) needs to be adjusted using a random value (d). If the total number of seats is too low, you need to decrease the denominator (d should be positive). If the total number of seats is too high, you need to increase the denominator (d should be positive).
Re-Calculate the total number of seats in the Adams Method -- And you have your apportionment!
An Example:
There are 10 Seats to be allocated. Population is 10 million.
Standard Divisor = s = Population/Seats = 1,000,000
In order to determine the allocation, the apportionment is rounded up.
The initial Adams calculation results in 11 seats being allocated, so the value of the standard divisor needs to be increased, so, through trial and error you must find a value of d such that the Adams apportionment has the correct number of seats.
In this example, a correct value of d is 50,000.
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Webster Method
This method uses the Arithmetic Rounding Scheme you learn in elementary school to determine the allocation.
The Process:
1. Find the standard divisor s by dividing total population/total seats.
2. Determine each states quota Q by dividing the state's population/standard divisor.
3. Use arethmetic rounding scheme to find each state's webster allocation.
Arethmetic mean when applied in rounding, when the quota is above the average of the two numbers (the lower number plus .5), round to the next highest integer. When the decimal point is below the average of the two numbers, round down to the lower integer.
4. Find the total number of seats that the intial webster method produces, if it's the inteded amount, great! You're done.
5. If not, the denominator (in the intital calculation, s) needs to be adjusted using a random value (d). If the total number of seats is too low, you need to decrease the denominator (d should be positive). If the total number of seats is too high, you need to increase the denominator (d should be positive).
6. Using trial and error, find a correct value of d, such that the total number of seats is correct. And then you've got your apportionment!
An Example:
There are 15 seats to be allocated. Population is 1,340.
Standard Divisor = s = Population/Seats = 89.33
In order to determine the allocation, the apportionment is rounded up if the decimal portion of population/standard divisor is .5 or above and rounded down if the decimal is below .5.
The initial Webster calculation results in 16 seats being allocated, so the value of the standard divisor needs to be increased, so, through trial and error you must find a value of d such that the Webster Apportionment has the correct number of seats.
In this example, a correct value of d is 2.67, so the denominator is 92.
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Dean Method
This Method Uses the Harmonic Mean to Determine Allocation.
The Process:
Find the standard divisor s By dividing total population/total seats
Determine each state's quota Q by dividing the state's population/standard divisor
Use harmonic rounding scheme to find each state's dean allocation
Harmonic Mean When applied in Rounding -- When the quota is Above the Harmonic Mean of the two numbers, round to the next highest Integer. When the decimal point is below the Harmonic Mean of the two numbers, round down to the lower integer.
4. Find the total number of seats that the intial Dean Method produces -- If It's the inteded amount, Great! You're Done.
5. If not, The denominator (in the intital calculation, s) needs to be adjusted using a random value (d). If the total number of seats is too low, you need to decrease the denominator (d should be positive). If the total number of seats is too high, you need to increase the denominator (d should be positive).
6. Using trial and error, find a correct value of d, such that the total number of seats is correct. And then you've got your apportionment!
An Example:
A Country has a Population of 11,882 with 21 Seats in Congress.
s = Population/Seats = 594.1
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