You will be writing a report addressing the following topics.
Part 1: Analyzing an Election
Select one of the results for the election you plan to analyze by going to my website or checking
the sheets in class. Your options are shown below.
Election Results
Justice League
Branches of the Military
Sports Leagues
Restaurants
Pixar Movies
1) Create a preference table for the election result data.
2) Describe the Plurality Method and determine the winner of the election. Make sure to show all
work.
3) Describe the Borda Count Method and determine the winner of the election. Make sure to
show all work.
4) Describe the plurality-with-elimination method and determine the winner of the
election. Make sure to show all work.
5) Describe the pairwise comparison method and determine the winner of the election. 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: Shapley Shubik Power Index
1) Find the Shapley-Shubik power distribution for the system [24: 17, 13, 11]
2) Find the Shapley-Shubik power distribution for the system [25: 17, 13, 11]
3) Write a short paragraph describing the Shapley- Shubik Power Index.
Part 3: 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.
Part 4: Honors section only!
1) Write a one-page paper comparing and contrasting Banzhaf Power Index and the ShapleyShubik Power Index. Make sure to be specific and detailed.
Other important stuff
1) You may either submit a hard copy or email me your report at brian.buri@robeson.k12.nc.us
2) Report should be in Times New Roman, 12 point font, double spaced, one inch
margins…Make it look nice and presentable.
3) You may do the work on a separate sheet of paper and turn it in with your rubric. You do not
need to type all of the work.
4) Project is due on Monday February 17th, 2014. You must turn in your rubric in order for me to
grade your project.
5) Make sure that your report is "nice-looking" and that you double check the rubric to make sure
you have addressed all required information.