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 |

1^{st} Choice |
A | C | D | B | C |

2^{nd} Choice |
B | B | C | D | D |

3^{rd} Choice |
C | D | B | C | B |

4^{th} 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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