MA 111 – Intro to Contemporary Mathematics
Circle One: Section 001 or Section 002
Quiz 3

An election is held in which there are four choices: A, B, C and D.  The preference schedule below shows the results.

# of Voters 14 10 8 4 1
1st Choice A C D B C
2nd Choice B B C D D
3rd Choice C D B C B
4th Choice D A A A A

1. How many people voted in the election?

37 people voted in this election.

2. How many votes are needed for a majority?  Is there a majority candidate?

Half of 37 is, 37/2=18.5, so 19 votes are necessary for a majority.  There is no majority candidate.

3. Is there a Condorcet Candidate?  If so, who?

Yes.  Candidate C beats every other candidate in a head to head competition, so she is the Condorcet candidate.

4. Who is the winner if we use the plurality method?

Candidate A has the most first place votes, and so he wins using the plurality method.

5. Who is the winner if we use the Borda method?

We assign 4 points for each first place vote, 3 for each second place vote, 2 for each third place vote and 1 for each last place vote.  When we do this, A has 79 points, B has 106, C has 104 and D has 81.  Hence, B is the winner when we use the Borda method.


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