# 39. Election A campus club needs to elect four officers: a president. a vice president. a secretary, and a treasurer. The club has five volunteers. Rather than vote individually for each position, the club members will rank the candidates in order of preference. The votes will then be tallied using the Borda count method. The candidate receiving the highest number of points will be president, the candidate receiving the next highest number of points will be vice president, the candidate receiving the next highest number of points will be secretary, and the candidate receiving the next highest number of points will be treasurer. For the preference schedule shown below, determine who wins each position in the club.

### Mathematical Excursions (MindTap C...

4th Edition
Richard N. Aufmann + 3 others
Publisher: Cengage Learning
ISBN: 9781305965584

Chapter
Section

### Mathematical Excursions (MindTap C...

4th Edition
Richard N. Aufmann + 3 others
Publisher: Cengage Learning
ISBN: 9781305965584
Chapter 4.2, Problem 39ES
Textbook Problem
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## 39. Election A campus club needs to elect four officers: a president. a vice president. a secretary, and a treasurer. The club has five volunteers. Rather than vote individually for each position, the club members will rank the candidates in order of preference. The votes will then be tallied using the Borda count method. The candidate receiving the highest number of points will be president, the candidate receiving the next highest number of points will be vice president, the candidate receiving the next highest number of points will be secretary, and the candidate receiving the next highest number of points will be treasurer. For the preference schedule shown below, determine who wins each position in the club.

To determine

Use Borda count method to determine who wins each position in the club.

### Explanation of Solution

Given Information:

 Rankings Cynthia â€ƒâ€ƒ4 â€ƒâ€ƒ2 â€ƒâ€ƒ5 â€ƒâ€ƒ2 â€ƒâ€ƒ3 Andrew â€ƒâ€ƒ2 â€ƒâ€ƒ3 â€ƒâ€ƒ1 â€ƒâ€ƒ4 â€ƒâ€ƒ5 Jen â€ƒâ€ƒ5 â€ƒâ€ƒ1 â€ƒâ€ƒ2 â€ƒâ€ƒ3 â€ƒâ€ƒ2 Hector â€ƒâ€ƒ1 â€ƒâ€ƒ5 â€ƒâ€ƒ4 â€ƒâ€ƒ1 â€ƒâ€ƒ4 Ahmad â€ƒâ€ƒ3 â€ƒâ€ƒ4 â€ƒâ€ƒ3 â€ƒâ€ƒ5 â€ƒâ€ƒ1 Number of votes: â€ƒâ€ƒ22 â€ƒâ€ƒ10 â€ƒâ€ƒ16 â€ƒâ€ƒ6 â€ƒâ€ƒ27

Concept used:

Use Borda count method to determine who wins each position in the club.

Calculation:

Each 1st place vote receive 5 points, each 2nd place vote receive 4 points, each 3rd place vote receive 3 points, ach 4th place vote receive 2 point, each 5th place vote receive 1 point, therefore,

Cynthia:

Andrew:

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