Math 110-01, Spring 2008 |
Assignment 4: Voting |
This assignment is due in class on Wednesday, February 13. This is an individual assignment. You can discuss the assignment with other people, but you should do the work on your own and you should write up your own answers. All answers should include explanations written out in full English sentences and paragraphs.
On the second page of the voting handout, it says: In the following example, alternative c is the Condorcet loser, yet wins the election under the Plurality method.
3 voters | 2 voters | 4 voters | |
first choice: | a | b | c |
second choice: | b | a | b |
third choice: | c | c | a |
Carefully explain what this means, why it is true, and why it is bad.
Suppose that an election is to be held in which there are four candidates, A, B, C, and D. There are 17 voters whose preferences are summarized in the following table:
Number of Voters |
First Choice |
Second Choice |
Third Choice |
Fourth Choice |
4 | C | B | A | D |
5 | B | C | A | D |
2 | A | C | D | B |
1 | A | D | B | C |
2 | D | B | A | C |
3 | D | C | B | A |
(a) Is there a Condorcet winner in this election? If so, who? Is there a Condorcet loser in this election? If so, who?
(b) Who, if anyone, wins this election under the Plurality voting method?
(c) Who, if anyone, wins this election under the Plurality with Runoff voting method?
(d) Who, if anyone, wins this election under the Plurality with Elimination voting method, using the Hare rule (in each round, eliminate the candidate with the fewest first-place finishes)?
(e) Who, if anyone, wins this election under the Borda Count voting method?
Suppose that you are running an election with three or more candidates (for a position in student government, say). After considering the various voting methods and their problems, what method would you propose to use for the election? Why? There is no right or wrong choice; just pick the method you like best and say why you think it is a good choice. However, your answer should reflect your understanding of the various options.