## Math 110-02, Spring 2014, Graded Homework #7

This is the final homework assignment for the course. it is due on the last day of class, Monday, May 5.

Part 1: Do the following exercises from Section 6.2:  6.2.8, 6.2.18, 6.2.25

Part 2: Do the following exercises from Section 10.4:  10.4.10, 10.4.11, 10.4.16

Part 3: For this part, consider the following table, which gives voter preferences for an election among alternatives A, B, C, and D:

 5 voters 10 voters 7 voters 3 voters First Choice A B C D Second Choice C D D A Third Choice D A B C Fourth Choice B C A B

(a) Which alternative wins using plurality voting? Why?

(b) Which alternative wins using plurality voting with runoff? Show your work.

(c) Which alternative wins using IRV (Instant Runoff Voting)? Show your work.

(d) Which alternative wins using the Borda Count? Show your work.

(e) Determine the winner in each of the six possible one-on-one matches. Is there a Condorcet winner (that is, an alternative that wins every one-on-one match)?

(f) Suppose that D is eliminated from the election. Is there a Condorcet winner among A, B, and C? Why?

Part 4: Be in class on Monday to turn in your work.