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 –

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