### DM 04 Election Theory Project

Sign-up for a GMAIL account if you do not already have one that includes your name in the username by clicking on the following link: GMAIL and then clicking on the RED button at the top right labeled "CREATE AN ACCOUNT."  Make sure that your username is professional, something that you would not mind sharing with a prospective employer.  Once completed, create a Microsoft Word document and name it "YOUR_NAME Election Theory Project."  You will be writing a report, addressing the following topics.

The rubric for this assignment can be viewed by clicking on the following link: Discrete Math Election Theory Project Rubric.

Part 1: Analyzing an Election

Select the results for the election you plan to analyze by clicking on the corresponding link in the following table.

 Election Results Justice League Branches of the Military Sports Leagues Restaurants Pixar Movies

1) Create a preference table for the election result data.  (Video: Creating a Preference Table in Word)

2) Describe the Plurality Method and determine the winner of the election if the method is used.  Make sure to show all work.

3) Describe the Borda Count Method and determine the winner of the election if the method is used.  Make sure to show all work.

4) Describe the plurality-with-elimination method and determine the winner of the election if the method is used.  Make sure to show all work.

5) Describe the pairwise comparison method and determine the winner of the election if the method is used.  Make sure to show all work.

6) What is Condorcet's criterion? Is the criterion satisfied if the plurality election method is used? Why?

7) What is the Majority criterion? Is the criterion satisfied if the Borda count method is used? Why?

Part 2: Analyzing a Weighted Voting System

Dan (D), Carol (C), Tamara (T), and Frank (F) are all members of the Euler Institute for Discrete Mathematics and its Applications (EIDMA) Executive Board.  To make decisions for the organization, a weighted voting system was created.  A total of 20 votes must be reached for any resolution to pass.  Dan's vote is worth 5, Carol's vote is worth 6, Tamara's vote is worth 8, and Frank's vote is worth 9.

1) Create a table listing all possible coalitions, the weight of each coalition, whether the coalition is a winning coalition or not, and which voters are critical in each coalition.  Use the first letter in a voter's name to represent the voter.

2) Find the Banzhaf Power Index (BPI) for each voter.

3) Write a paragraph summarizing your findings.  Be sure to rank each voter from the most powerful to the least powerful.

4) Make sure that your report is "nice-looking" and that you double check the rubric to make sure you have addressed all required information.  Then, save your report as a PDF by clicking "Save As" and then the clicking on "PDF."  Make sure that both the PDF and the word document are titled "YOUR_NAME election theory project."

5) While logged into your GMAIL account that you created, go to drive.google.com and click on the the SHARED WITH ME link at the left.  In this section you should see a folder with your name listed in the order last name first name.   Click on the folder to open it, then upload both your word document and your pdf by clicking on the red upload button directly next to the red "create" button.  Once this process is completed, you have submitted your project.  Congratulations! You have completed your first project!