# Chapter 4 - Review Sheet - The Mathematics of Apportionment

## Definitions -

Adam’s
Method

Alabama Paradox

Apportionment
Method

Balinski and Young’s Impossibility Theorem

Hamilton’s Method

Jefferson’s Method

Lower
Quota

Lower-Quota
violation

Modified
Divisor

Modified
Quota

New-states
Paradox

Population
Paradox

Quota
Rule

Standard
Divisor

Standard
Quota

Upper
Quota

Upper-Quota
Violation

Webster’s
Method

## Examples -

Hamilton’s Method

Jefferson’s Method

Adams’Method

Webster’s
Method

Alabama Paradox

New-states
Paradox

Population
Paradox

## Concepts -

Methods
that favor large states

Methods
that favor small states

Methods
that can violate Alabama Paradox

Methods
that can violate New-states Paradox

Methods
that can violate Population Paradox

Methods
that can violate the lower quota rule

Methods
that can violate the upper quota rule

When
the standard divisor is increased the standard quotas decrease.

When
the standard divisor is decreased the standard quotas increase.

The
sum of the standard quotas is equal to the quantity that is being apportioned.

Based
on the 2000 U.S. Census, there are 646,952 people per representative.

Hamilton’s Method was supposed to be the first
apportionment method to be used by the United
States, but President Washington vetoed Hamilton’s
Method and chose Jefferson’s Method instead.
The first presidential veto was of Hamilton’s
Apportionment Method. The reason for vetoing Hamilton’s Method.

Problems
–

Page
150 #1, 5, 7, 11, 19, 23, 31, 33, 41, 43