Math 118 G1 Writing Project

Due: April 14, 2006

Chapter 9 discusses several different ways of determining the results of an election when more than two candidates are running. We will be discussing each of these methods in class, along with their strengths and weaknesses.

In addition to the homework problems from the chapter which will give you some practice determining the winner of an election, you will be setting up an election yourself and determining the winner using the results of this chapter. This will give you a chance to see how the different voting methods turn out.

Here is what you need to do:

1. Decide on an issue that you will use in your election. You should come up with at least four "candidates", though you don't want to have too many. For example, you can try to determine the most popular season of the year, or the best holiday. Try to be creative, and be sure to pick a topic where it is possible to rank all of the candidates using preference lists (i.e., don't pick something like "Should we get rid of Chief Illiniwek?").
2. Ask at least ten people to rank the candidates in your election, using preference lists. You should explain to them that they need to rank all of the candidates, and that they can't have ties. Even if they are indifferent between two choices, they need to pick an order.
3. Use the four methods from class (plurality, Borda count, sequential pairwise voting, and the Hare system) to determine the winner of the election. You may find that different methods result in different winners. Find all of the results of the election, not just the winner in each case (i.e., how did each candidate do with each method).
4. Write a one page essay describing the election you chose, the different outcomes, and which method you think seems most fair for your election.

If you wish, you may work with one other person in setting up the election and asking people to vote, but I want you each to determine the results of the election and write separate essays. You may NOT both turn in the same essay.

This project is worth 40 points, applied to your homework grade:

• 10 points for setting up the election
• 10 points for determining the winners
• 20 points for the essay, graded both for mathematical content and clarity

Use common sense when typing your essay; huge margins and huge typefaces will not be tolerated. I am more concerned with what you write than how much you write, but you need to write about one page to get full credit.

If you have any questions about this assignment, please see me before or after class, in my office, or email me.