A barbershop quartet is electing a new leader. Each member of the group is given a ballot to rank each member of the quartet to decide who should be the leader. Each member's first choice is listed at 1 and their last choice is listed as 4. Here is a summary of the data. Member Ballot A Ballot Ballot C Ballot Fiery Flo 1 2 1 2 Big Bass 3 4 3 3 Baritone Atta 2 1 2 4 Atomic Tilly 4 3 4 1 Use the Borda Count System to determine who will be the new leader of the quartet.

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### Electing a New Leader for the Barbershop Quartet

A barbershop quartet is electing a new leader. Each member of the group is given a ballot to rank each member of the quartet to decide who should be the leader. Each member’s first choice is listed as 1 and their last choice is listed as 4. Here is a summary of the data:

| **Member**      | **Ballot A** | **Ballot B** | **Ballot C** | **Ballot D** |
|-----------------|--------------|--------------|--------------|--------------|
| Fiery Flo       | 1            | 2            | 1            | 2            |
| Big Bass        | 3            | 4            | 3            | 3            |
| Baritone Atta   | 2            | 1            | 2            | 4            |
| Atomic Tilly    | 4            | 3            | 4            | 1            |

### Explanation of Borda Count System

The Borda Count System is a ranked voting method in which voters will rank the options (in this case, the quartet members) in order of preference. Points are then allocated based on the rankings. For example, in a vote with 4 options:
- 1st choice gets 3 points (N-1 where N is the number of candidates),
- 2nd choice gets 2 points,
- 3rd choice gets 1 point,
- 4th choice gets 0 points.

### Calculating Borda Count Points

Using the Borda Count System to determine the new leader, we will assign points based on the rankings each member received:

#### Fiery Flo
- Ballot A: 1st (3 points)
- Ballot B: 2nd (2 points)
- Ballot C: 1st (3 points)
- Ballot D: 2nd (2 points)
- **Total Points = 3 + 2 + 3 + 2 = 10 points**

#### Big Bass
- Ballot A: 3rd (1 point)
- Ballot B: 4th (0 points)
- Ballot C: 3rd (1 point)
- Ballot D: 3rd (1 point)
- **Total Points = 1 + 0 + 1 + 1 = 3 points**

#### Baritone Atta
Transcribed Image Text:### Electing a New Leader for the Barbershop Quartet A barbershop quartet is electing a new leader. Each member of the group is given a ballot to rank each member of the quartet to decide who should be the leader. Each member’s first choice is listed as 1 and their last choice is listed as 4. Here is a summary of the data: | **Member** | **Ballot A** | **Ballot B** | **Ballot C** | **Ballot D** | |-----------------|--------------|--------------|--------------|--------------| | Fiery Flo | 1 | 2 | 1 | 2 | | Big Bass | 3 | 4 | 3 | 3 | | Baritone Atta | 2 | 1 | 2 | 4 | | Atomic Tilly | 4 | 3 | 4 | 1 | ### Explanation of Borda Count System The Borda Count System is a ranked voting method in which voters will rank the options (in this case, the quartet members) in order of preference. Points are then allocated based on the rankings. For example, in a vote with 4 options: - 1st choice gets 3 points (N-1 where N is the number of candidates), - 2nd choice gets 2 points, - 3rd choice gets 1 point, - 4th choice gets 0 points. ### Calculating Borda Count Points Using the Borda Count System to determine the new leader, we will assign points based on the rankings each member received: #### Fiery Flo - Ballot A: 1st (3 points) - Ballot B: 2nd (2 points) - Ballot C: 1st (3 points) - Ballot D: 2nd (2 points) - **Total Points = 3 + 2 + 3 + 2 = 10 points** #### Big Bass - Ballot A: 3rd (1 point) - Ballot B: 4th (0 points) - Ballot C: 3rd (1 point) - Ballot D: 3rd (1 point) - **Total Points = 1 + 0 + 1 + 1 = 3 points** #### Baritone Atta
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