### Preliminary Ideas: Terminology and Notation

Apportionment

Apportionment is the process of allotting identical, indivisible objects among participants entitled to unequal shares.

Standard Divisor

The Standard Divisor is the average number of people per seat over the entire population.

Standard Quota

The Standard Quota is the fraction of the total number of seats a state would be entitled to if the seats were not indivisible.

Note: SD is the Standard Divisor.

Note: Each State has a Standard Quota.

Lower Quota: The Standard Quota rounded down

Upper Quota: The Standard Quota rounded up

Quota Rule

An apportionment method that always allocates only lower and/or upper bounds is called a quota rule.

A particular apportionment that doesn't allocate only lower and/or upper bounds is said to 'violate quota'.
An apportionment method with which it is possible to 'violate quota' is said to 'violate the Quota Rule'(regardless of whether any particular apportionment using that method actually does so).

### The Arithmetic Mean and the Geometric Mean are used in rounding rules for two of the apportionment methods we will be concerned with.

The ARITHMETIC MEAN (or AVERAGE) of 2 numbers a & b is defined by:

Ex: Find the arithmetic mean between 4 & 9.

AVG = (4 + 9) / 2 = 13 / 2 = 6.5

The GEOMETRIC MEAN, GM, of 2 numbers a & b is defined by:

Ex: Find the geometric mean between 4 & 9.

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