Eleven seats on a condominium association board for buildings Amity, Buddy, and Chum are to be apportioned.
Current Representation:
Amity Buddy Chum
1 800 2113 4050
2 267 704 1350
3 133 352 675
4 80 211 405
5 53 141 270
Use the given table of Huntington-Hill numbers to list the order in which the seats on the board will be apportioned. For example: ABCCABABC
How do I list the order? I do not know how to do this problem.
To list the order in which the seats on the board will be apportioned using the given table of Huntington-Hill numbers, you need to follow a specific algorithm called the Huntington-Hill method. Here's how you can approach this problem:
Step 1: Calculate the initial quotas for each building by dividing the population of each building by the geometric mean of its current representation and its current representation plus one. The geometric mean is the square root of the product of the current representation and its current representation plus one.
Step 2: Compare the initial quotas of all buildings and assign the first seat to the building with the highest initial quota.
Step 3: Recalculate the quotas for all buildings by dividing the population of each building by the geometric mean of its current representation plus one and its current representation plus two.
Step 4: Compare the recalculated quotas of all buildings and assign the second seat to the building with the highest recalculated quota.
Step 5: Repeat steps 3 and 4 until all eleven seats have been assigned.
To determine the order in which the seats are apportioned, you can use the following notation:
- A represents a seat being allocated to Amity
- B represents a seat being allocated to Buddy
- C represents a seat being allocated to Chum
For example, if the first seat is allocated to Amity, the second seat to Buddy, the third to Chum, the fourth and fifth to Amity, and so on, the order would be ABCCA.
By following the Huntington-Hill method described above, you can continue assigning seats until all eleven seats have been apportioned and determine the exact order, using the notation provided.