# Section 17.3: Apportionment

## 17.3 Outline

1. Definition of apportionment
2. The apportionment process
1. upper quota
2. lower quota
3. standard divisor
4. standard quota
5. quota rule
1. definition
2. modified divisor
3. modified quota
4. Jefferson’s plan
5. Hamilton’s plan
6. Webster’s plan
7. Hungtington-Hill plan
1. arithmetic mean
2. geometric mean
8. Summary of apportionment methods

## 17.3 Essential Ideas

To find the standard divisor divide the total population by the shares (or number of representatives). To find the standard quota divide the total population by the standard divisor.

The Quota Rule

The number assigned to each represented unit must be either the standard quota rounded down to the nearest integer, or the standard quota rounded up to the nearest integer.

Any standard quota with a decimal portion must be rounded up to the next whole number. Use a modified divisor to come up with the appropriate number of seats.

Jefferson’s Plan

Any standard quota with a decimal portion must be rounded down to the next lower whole number. Use a modified divisor to come up with the appropriate number of seats.

Hamilton’s Plan

The standard quotas are rounded down, but each must be at least one. Give additional seats, one at a time, until no seats are left. These are given, in order, to the states with the largest fractional parts of their standard quotas.

Webster’s Plan

The standard quotas are rounded to the nearest whole number using the arithmetic mean. Use a modified divisor to come up with the appropriate number of seats.

Huntington-Hill’s (HH) Plan

The standard quotas are rounded to the nearest whole number using the geometric mean. Use a modified divisor to come up with the appropriate number of seats.