Math 101: Topics in Mathematics
Guide for Exam 2

The second midterm is on Wednesday, November 12, during the regular class period.

The following is a chapter by chapter guide intended to help you organize the material we have covered as you study for your exam. It is only intended to serve as a guideline, and may not explicitly mention everything that you need to study.

Please start by taking a look at class notes and the material that we discussed in class. Then review all relevant textbook sections and homework problems for the chapters given below, and make sure you can solve all of them.

Ch 9.1-9.3. Voting Systems:

  1. Know how to determine the winner of an election using the following systems:
    1. Majority Rule
    2. Condorcet's Method
    3. Plurality Voting
    4. Borda Count
    5. Sequential Pairwise Voting
    6. Hare System
    7. Plurality Runoff Voting
  2. You do not need to review the fairness criteria for this exam.

Ch 10.1-10.3. Manipulability of Voting Systems:

  1. Know the definition of manipulability and how it applies to the following systems:
    1. Borda Count
    2. Sequential Pairwise Voting
    3. Hare System
    4. Plurality Runoff Voting
  2. You should also know how to determine whether a described voting system is manipulable or not.

Ch 11.1-11.4. Weighted Voting Systems:

  1. Know the notation for weighted voting systems and the definitions of the following terms:
    1. Dummy Voter
    2. Dictator
    3. Veto Power
    4. Voting Combination
    5. Critical Voter
    6. Voting Permutation
    7. Pivotal Voter
  2. Know how to compute:
    1. Banzhaf Power Index
    2. Shapley-Shubik Power Index
  3. You should also know how to determine whether two weighted voting systems are equivalent or not.

Ch 14.1-14.3. Apportionment:

  1. Know how to determine the following in an apportionment problem:
    1. States
    2. Populations
    3. House Size
    4. Standard Divisor
    5. Quota
  2. Know how apportionments are made using the following:
    1. Hamilton Method
    2. Jefferson Method
  3. Know the definitions of the following criteria and whether or not they are satisfied by the methods above:
    1. House Monotone
    2. Population Monotone

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