Mathematics

### What You Should Be Able To Do For Test 1

#### "For All Practical Purposes," Chapter 15

Apportion a legislature, etc., using Hamilton's method, Jefferson's method, Webster's method, or the Hill-Huntington method.

In examples, tell whether the Alabama paradox or the population paradox occurs, or whether the quota condition is violated.

Compare absolute and relative difference in district size.

#### "For All Practical Purposes," Chapter 12

Find the winner of an election using (1) plurality voting, (2) Borda count, (3) the Hare system, (4) sequential pairwise voting with a given agenda.

Answer questions such as: Does this example violate the Condorcet winner criterion? Independence of Irrelevant Alternatives? Monotonicity? The Pareto Condition?

Some of the voting methods always satisfy certain of the fairness criteria. You should be able to explain why.

#### Personal Help Sheet

You may bring to the test one sheet of paper containing whatever you find helpful.

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