1. Defining different types of voters

   1. Critical, pivotal, dummy, and dictator voters

   2. Examples of each type

2. Defining weighted voting

   1. Examples of how weighted voting relates to the different types of voters

3. OPTIONAL: connection to literature: Animal Farm

   1. If possible, have students reading this book at the same time as learning the material

   2. Discussion questions: were the commandments that the animals created followed by all animals?

      1. How does weighted voting connect to the idea that: "all animals are created equal, but some are more equal than others" - chapter 10, page number 112

4. Homework:

   1. What is the difference between a critical voter and a pivotal voter?

   2. Fill in the blank:

      1. A voter who is critical in a winning coalition is ______ voter.

2. 1. 1. A voter who is never critical in a winning coalition is _____ voter.

3. Is the electoral college weighted?

4. Does this make sense? [7: 5, 5, 4, 2]

5. OPTIONAL: What type of animals had the most power in Animal Farm? Why? Could these animals be considered dictators?

5. Additional Resources:

https://jtcc.edu/downloads/services/math-center/MTH170WeightedVoting.pdf

http://www.people.vcu.edu/~gasmerom/MAT131/lecture2.html

1. Defining what a coalition is - what makes a coalition a winner or a loser

   1. Example of how to compute whether a coalition wins or loses

2. How does a critical voter connect to a coalition

   1. Review of what a critical voter is

   2. Two examples that highlight the role of a critical voter

3. Defining sequential coalitions

   1. Two examples that illustrate that the order in which a voter joins matters

4. OPTIONAL: connection to literature: Animal Farm

   1. Discussion question: Did the animals form a coalition to "overthrow" Mr. Jones?

5. Homework:

   1. Create your own example of a winning coalition and a losing coalition

   2. How is a sequential coalition different than a regular coalition?

   3. OPTIONAL: In the later chapter of Animal Farm, were additional coalitions created? Were there any types of animals that proved to be critical members?

6. Additional Resources:

http://www.math.wisc.edu/~robbin/141dir/propp/COMAP/Guidefor1stTimeInstructors/l_FAPP07_FTI_11.pdf

1. Introduction to Banzhaf Method

2. Reviewing critical voters

1. Critical voters - What makes a voter critical in Banzhaf Method?

2.What is the quickest way to know the number of possible coalitions?

3. Listing out winning coalitions in Banzhaf Method

3. Computing the Banzhaf Power Index

1. Steps to take

2. Important tips in computation

3. Examples of computation

4. Examples of Application: Electoral College and European Economic Community

5. Youtube tutorial

4. Homework

5. Additional Resources

1. https://en.wikipedia.org/wiki/Banzhaf_power_index#:~:text=Banzhaf%20III%20(originally%20invented%20by,necessarily%20equally%20divided%20among%20the

2. https://math.libretexts.org/Bookshelves/Applied_Mathematics/Book%3A_Math_in_Society_(Lippman)/03%3A_Weighted_Voting/3.04%3A_Calculating_Power-__Banzhaf_Power_Index

3. http://www.cs.unc.edu/~livingst/Banzhaf/

4. http://jlmartin.faculty.ku.edu/~jlmartin/courses/math105-F11/Lectures/chapter2-part2.pdf

5. https://www.sciencedirect.com/science/article/pii/S0895717708001799

1. Reviewing weighted voting

   1. Pivotal voters - How are they different from critical voters?

   2. Sequential coalitions - How to find them, how they are different from coalitions in Banzhaf

2. Defining the Shapley-Shubik Power Index

   1. Measuring the power of when a voter joins a coalition

   2. Emphasize that order matters, unlike in Banzhaf

3. Computing the Shapley-Shubik Power Index

   1. Video example

   2. Two site examples

   3. Optional: UN Security Council

4. Homework:

   1. A committee consists of four members, A, B, C and D. Each member of the committee has one vote except for the chairperson (A) who has veto power. A measure needs a minimum of two votes to pass (one of which must be the chairperson's). What is the Shapley-Shubik distribution in this committee?

   2. Show that the Shapley-Shubik indices for (6: 4,3,2,1) are the same as the Banzhaf indices.

   3. Calculate the Shapley–Shubik power index for each of the voters in the weighted voting system V(20; 11, 8, 7, 3).

   4. Calculate the Shapley–Shubik power index for each of the voters in the weighted voting system V(6; 3, 2, 2, 2, 2).

5. Additional Resources:

   1. https://en.wikipedia.org/wiki/Shapley%E2%80%93Shubik_power_index

   2. https://www.math.colostate.edu/~spriggs/m130/power2.pdf

   3. https://math.libretexts.org/Bookshelves/Applied_Mathematics/Book%3A_Math_in_Society_(Lippman)/03%3A_Weighted_Voting/3.05%3A_Calculating_Power-__Shapley-Shubik_Power_Index

   4. http://jlmartin.faculty.ku.edu/~jlmartin/courses/math105-F11/Lectures/chapter2-part2.pdf