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 |

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

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

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

4^{th} 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 |

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

2^{nd} 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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