MMW: Apportionment and Voting

Apportionment

is a method of distributing a number of items proportionally into several groups based on population sizes.

Hamilton Method

Is based on standard divisor and standard quota of the population.

alexander hamilton

who proposed the hamilton method?

SD = P/A

standard divisor (SD) formula

Total population

“P” represents what?

total number to be apportioned

“A” represents what?

SQ = G/SD

standard quota (SQ) formula?

Size of the group

“G” represents what?

divisor

“SD” represents what?

lower quota

The whole number portion of the standard quota is called

Round down the standard quota to a whole number

How to get the lower quota of a group?

If the sum of the lower quotas is less than the value of A (total number to be apportioned)

The standard quota of a group with the highest decimal part is only rounded up to a whole number if?

Jefferson Method

Uses a modified standard divisor (MSD) which is chosen by trial and error until the sum of the lower quotas is equal to the required number of allocations.

Lower Quota

is the final apportionment obtained at the final value of the modified divisor

Jefferson Method

In this method, the modified standard divisor is smaller than the original standard divisor.

Webster Method

used ordinary rounding, making it completely unbiased. The modified standard divisor is determined using trial and error.

Huntington-Hill Method

uses the geometric means to round standard quotas until the sum of of the modified quotas equals the exact number of seats to be apportioned.

multiply the upper and lower quotas then get the square root

How to get the geometric mean?

highest Huntington-Hill number

When there is a need to add one item to one of the several groups in a population, the additional one item is given to the group with the highest?

H = G^2 / A(A+1)

huntington-hill number formula

G = Size of group

A = Current number of items assigned to the group

in huntington-hill number formula, what does “G” and “A” represent, respectively?

TRUE

TRUE or FALSE: The Hamilton Method always satisfies the quota criterion

True

True/False \n The Webster method rounds the quotas to the nearest whole number.

True

True/False \n In the Hamilton method the first surplus seat is assigned to the state with the largest fraction after the original division.

False

True/False \n The Huntington-Hill method uses upper and lower quotas in traditional rounding to assign representatives for each states.

False (The Jefferson method of apportionment divides all populations by a modified divisor and then rounds the results up to the __**LOWER**__ quota.)

True/False \n The Jefferson method of apportionment divides all populations by a modified divisor and then rounds the results up to the upper quota.