Math 105 Video 5.1a Intro to Apportionment

Introduction to Apportionment

Apportionment is the problem of dividing a fixed number of indivisible items or people among groups of different sizes. A key example is distributing seats in the U.S. House of Representatives among the 50 states, whose populations vary.

Rules of Apportionment

1. Assignments must be whole numbers. Items such as representatives, school buses, or gold coins cannot be split into fractions. This makes apportionment more difficult than dividing something like money, which can be divided using decimals.

2. Use the exact total available. The allocation must assign every available item—no more and no fewer.

3. Every group must receive at least one. Even a small group cannot be assigned zero items under this rule.

4. Allocations should be proportional to group size. Larger groups should generally receive more, and smaller groups less. For example, a state with about one-quarter of the population should receive about one-quarter of the representatives. Because assignments must be whole numbers, exact proportionality may not be possible; the goal is to get as close as possible.

The video introduces these rules and notes that later videos will cover apportionment methods and examples.

Speaker and Source

• Instructor/narrator: Cara Lee, identified from the channel metadata.