Abstract

       Before the year ends, you're looking for a good music playlist for all of your friends and family to enjoy in those last few minutes on New Years Eve. The conflict, however, is that most of the people you know have very different music tastes and interests making it extremely hard for you to choose the right music. Because it's New Year's Eve, you really do want to please most, if not, all of your guests, so what you do is ask them to fill out a survey on a playlist you've put together which includes ten very different songs. You will play all of the songs before the year ends but it will be based on your guests' votes and depending on which song is ranked the highest, the playlist will then be played from least favorite song to most favorite to end the the year off enjoying some great music. 

Playlist

The playlist consists of these 10 songs:

- Maroon 5: Animals

- Coldplay: Sky Full Of Stars

- Phoenix: 1901

- The Killers: Mr. Brightside

- Ed Sheeran: Sing

- The 1975: Chocolate

- Sam Smith: Stay With Me

- Enrique Iglesias: Bailando

- 5 Seconds of Summer: She Looks So Perfect

- Benny Benassi: Cinema

 

But how did we get that?

• The Plurality Method
• The Borda Count Method

In this survey, I used two major methods of election for selecting which song was the most popular which determined how the playlist would be set up. They were:

The Plurality Method

• We decide the winner by counting only the first place votes.
• The candidate with the most first place votes is the winner. 
• This the method we use for real elections

This method is the most commonly used in our everyday lives when trying to decide on a variety of options. The way that this method works is:

THE PLURALITY METHOD

Candidates

First Place Votes

Animals

The 1975

Killers

Enrique Iglesias

Sam Smith

Sky Full of Stars

Benny Benassi

5 Seconds of Summer

Ed Sheeran

1901

(Out of 35 People)

8

6

5

5

4

2

2

1

1

1

Why do we use THE PLURALITY METHOD?

• According to the plurality method, "Animals by Maroon 5" is the winner. But why exactly do we use this method to calculate this?
  • One reason we do so is because it's not only VERY useful but also very quick and not time consuming.
  • The only drawback to this method is that it does not take into account people's other choices.
    • Someone could've had this song as their last choice but since because most people voted it as first, it wins anyway

What is another method?

Another possible method we could use is the Borda Count Method.

The Borda Count Method

Now, we will do the same thing using the Borda Count Method. But what is this method?

• This method uses another way to determine the winner by assigning points to each candidate based on it's rank on each ballot . 
• A candidate would get more points for being ranked higher on the ballot than a candidate below it. 
• The points are assigned so a first place vote gets as many votes as the number of candidates.  
• Each place below first place receives one point less.
• It is named after french Jean-Charles de Borda.  

THE BORDA COUNT METHOD

Now, with only the first three choices from the playlist which are "Animals" (A), "Chocolate" (C), and "Mr. Brightside" (M), we'll see how the Borda Count Works:

# of Votes

4    5    6    8

1st Choice

2nd Choice

3rd Choice

M    M    A    C

A    A     C    A

C    A    M    M

2

1

0

THE BORDA COUNT METHOD

Now, we will multiply the number of votes by the last place votes which go up by 1 starting at zero for each of the song choices and see which one is elected off of the top 3 choices. Once multiplied, we will end up the the totals:

(M) Mr. Brightside = 8 + 10 + 0 + 0 = 18

(A) Animals = 4 + 5 + 8 + 12 = 29

(C) Chocolate = 0 + 0 + 6 + 16 = 22

Once again, with using a different method, "Animals" is still the most voted song and won the election

Why do we use the borda count method?

The use the Borda Count Method, apart from just the common plurality method for a few important reasons:

• It's useful for taking into account all of the information from the preference ballots
• And it gives a ranking of the candidates rather than just a single winner.  

The PLaylist Problem

So, in the end, even though there was an overall winner of who was the favorite song, all the songs will be played at the event but just based on what order they were put in using both the Plurality method and the Borda Count Method. The Final New Years Eve Playlist would look like this:

1. Maroon 5: Animals

2. The 1975: Chocolate

3. The Killers: Mr. Brightside

4. Enrique Iglesias: Bailando 

5. Sam Smith: Stay With me

6. Coldplay: Sky Full of Stars

7. Benny Benassi: Cinema

8. 5 Seconds Of Summer: She Looks So Perfect

9. Ed Sheeran: Sing

10. Phoenix: 1901

The end