The number of representatives from each state in the U.S. House of Representatives is proportional to the state's population, and this number is updated every 10 years. Several different methods, called methods of apportionment, have been used to decide how many representatives each state should have.

Apportionment methods are useful in any situation where a small number of delegates (or representatives) are chosen to represent a larger population that consists of separate groups, in a manner consisten with the size of those groups.

Usually it is not possible to find a perfect method of apportionment, so the resulting choice is a combination of math and politics.

The **standard divisor** is the total population divided by the
total number of seats:

*standard divisor = total population / total number of seats*

It's the average number of people represented by any one House member.

A state's **standard quota** (is also called its **exact
quota**), is the number obtained by dividing the state's population by
the standard divisor:

*standard quota = state's population / standard divisor*

If we substitute the standard divisor into the above equation, we see the alternate
formula:

standard quota = total number of seats * (state's population / total population)

**Quota methods** of apportionment work with the standard divisor
and round-off standard quotas, according to some rules. Rounding down the standard
quota to an integer gives the **lower quota **and rounding up gives
the **upper quota**.

**Hamilton's Method**

Hamilton's method consists of assigning the lower quota (except when it is 0)
to each state at first, and then assigning any remaining seats to the states
whose standard quotas have the largest fractional part.

1. Find the standard divisor

2. Find each state's standard quota

3. Assign the lower quota to each state, unless it is 0. In this case, assign
1.

4. If there are any seats remaining, find the state with the largest fractional
part of the standard quota (excluding states that had 0 as lower quotas). If
there are still remaining seats, assign the next seat to the state with the
next largest fractional part. Continue this way until all are assigned.

**Lowndes' Method
**Lowndes' method is similar to Hamilton's method, except it uses the

1. Find the standard divisor

2. Find each state's standard quota

3. Assign the lower quota to each state, unless it is 0. In this case, assign 1.

4. If there are any seats remaining,