MA 111 – Intro to Contemporary Mathematics
Circle One: Section 001 or Section 002
Quiz 2

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

# of Voters 12 14 5 3 8 2 1 9 13 5
1st Choice A A A B B B C C C D
2nd Choice B C B C C D A B D A
3rd Choice C B D A D A B D B B
4th Choice D D C D A C D A A C

1. How many people voted in the election?

12+14+5+3+8+2+1+9+13+5=72 people voted in the election.

2. Which candidate got the most first place votes?

Candidate A received 31 first place votes.  No other candidate received more.

3. Which candidate got the fewest last place votes?

Candidate B received zero last place votes.

4. Who would have the most first place votes if only candidates A and D participated in the election?

Removing candidates B and C results in the preference schedule below (remember, when a candidate is eliminated, we bump up those below him or her without changing their order).

# of Voters 12 14 5 3 8 2 1 9 13 5
1st Choice A A A A D D A D D D
2nd Choice D D D D A A D A A A

Then when we recalculate the numbers of first place votes we see that A receives 35 votes and
D receives 27 votes.  So candidate A would win the head to head election between A and D.


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