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Apportionment involves dividing something up, just like fair division. In fair division we are dividing objects among people while in apportionment we are dividing people among places. Also like fair division, the apportionment processes that are widely used do not always give the best answer, and apportionment is still an open field of mathematics. Apportionment is used every day in American politics. It is used to determine the size of voting districts and to determine the number of representatives from each state in the U.S. House of Representatives. Another example of how apportionment can be used is to assign a group of new fire fighters to the fire stations in town in an equitable way. Overall, apportionment is used to divide up resources (human or otherwise) in as fair a way as possible.
- 9.1: Apportionment - Jefferson’s, Adam’s, and Webster’s Methods
- Apportionment can be thought of as dividing a group of people (or other resources) and assigning them to different places.
- 9.2: Apportionment - Jefferson’s, Adams’s, and Webster’s Methods
- Jefferson’s, Adams’s, and Webster’s methods are all based on the idea of finding a divisor that will apportion all the seats under the appropriate rounding rule. There should be no seats left over after the number of seats are rounded off. For this to happen we have to adjust the standard divisor either up or down. The difference between the three methods is the rule for rounding off the quotas.
- 9.3: Apportionment Paradoxes
- Each of the apportionment methods has at least one weakness. Some potentially violate the quota rule and some are subject to one of the three paradoxes.