Answer to Question #139388 in Operations Research for Ethan

Question

A. Describe apportionment.
B. What are the different methods of apportionment? Describe each method.
C. Define Huntington-Hill Number.

Answer 1

Apportionment is the act of dividing costs between different accounts in a fair way, or the amount that is put into each account.

Methods of apportionment:

Hamilton’s Method:

• Step 1. Calculate each state’s lower quota.
• Step 2. Round the standard quota’s down and give to each state its lower quota
• Step 3. Give the surplus seats (one at a time) to the states with the largest residues (fractional parts) until there are no more surplus seats.

Jefferson’s Method

• Step 1: Find a ‘suitable’ divisor d.
• Step 2: Using d as the divisor, compute each state’s modified quota (modified quote = state population/d).
• Step 3: Each state is apportioned its modified lower quota. 

Adam’s Method

• Step 1: Find a ‘suitable’ divisor d.
• Step 2: Using d as the divisor, compute each state’s modified quota (modified quota = state population/d).
• Step 3: Each state is apportioned its modified upper quota.

Webster’s Method

• Step 1: Find a ‘suitable’ divisor d.
• Step 2: Using d as the divisor, compute each state’s modified quota (modified quote = state population/d).
• Step 3: Find the apportionments by rounding each modified quota to the nearest integer.

Huntington-Hill Method

• Step 1: Find a ‘suitable’ divisor d. [Here a suitable divisor means a divisor that produces an apportionment of exactly M seats when the quotas (populations divided by d) are rounded using the Huntington-Hill rounding rule.]
• Step 2: Find the apportionment of each state by rounding its quota using the Huntington-Hill rounding rule.

Define Huntington-Hill Number: