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The Correlation and Line of Best Fit between a Political Leaders’ Facial Proportions and their General Election Popularity

### Introduction

Beauty is in the eye of the beholder. Is that always true? As someone interested in political science, I often wonder about elections and what qualities are exhibited by a strong leader. Charisma and attractiveness is seen to be the most important factor. In the elections of the USA between Nixon and JFK, the television revolutionized elections. Most people who watched the debate on television agree that JFK commanded the audience better and had a more calm and relaxed performance next to Nixon’s stutters and nervous sweats. JFK won the election that year. He is also seen as the most charismatic and most attractive president of the USA. Does beauty truly matter?

Beauty is in the eye of the beholder. How can a statement so well-known be wrong? Regardless of culture, region, location, or beliefs, beauty rules and norms such as the fibonacci sequence and the golden mean are universal. But does beauty matter in terms of general elections? Was the legendary presidential election between Nixon and JFK really determined through the television? In this investigation I will determine the correlation, if any, between physical, facial beauty and electoral popular votes (percentages).

Data will be collected for leaders in 4 different regions, Western, Asian, African, and Hispanic, each a similar age and a similar position of power. After leaders are selected I will find headshot photos and measure the ratios from the eyes to the edge of the face, the nose to the mouth, the mouth to the side of the face, and the front left tooth to the 2nd left tooth. After calculating and finding these ratios, I will then collect data on the percentage votes from their most recent elections. I will then determine which one of these leaders is considered most beautiful based on their average ratio, and which one of these leaders is most popular based on the average percentage votes. I will then graph each of my measurements as coordinate points on a Cartesian plane where the x-axis represents the percentage points and the y-axis represents the ratios of the face. I will then determine a correlation between beauty and political power, and using charts and data, calculate the line of best fit, which will determine an equation that calculates a beauty ratio based on the percentage votes in an election.

Body

I have selected 4 different leaders from Western, Asian, African, and Hispanic regions. The Western leader will be Justin Trudeau: the prime minister of Canada, at the age of 46. The Asian leader will be Shinzō Abe: the prime minister of Japan, at the age of 64. The African leader will be Jacob Zuma: the president of South Africa, at the age of 76. The Hispanic leader will be Sebastián Piñera: the president of Chile at the age of 69.

Through measurements (in millimeters) I have calculated each one of these ratios in every leader: from the eyes to the edge of the face, the nose to the mouth, the mouth to the side of the face, and the front left tooth to the 2nd left tooth. I collected and measured pictures with a relaxed face, and a picture with a smiling face, for each leader, and I found each ratio in the chart below:

Eyes: Edge of the Face

Mouth: Nose

Mouth: Side of the Face

Front Left Tooth: 2nd Left Tooth

### Justin Trudeau

16mm:13mm

30mm:21mm

30mm:18mm

2mm:1.5mm

Shinzō Abe

14mm:10mm

21mm:19mm

21mm:18mm

2mm:2mm

Jacob Zuma

9mm:5mm

28mm:23mm

28mm:17mm

3mm:2mm

Sebastián Piñera

7mm:6mm

19mm:15mm

19mm:12mm

1.6mm:1mm

The results from this graph are of my own measurements of pictures found in Google Images on the internet; therefore, there may be a potential human error in my measurements, as I had taken these measurements with a ruler. Given a longer period of time, I could have used more accurate means of measurement, such as the Fibonni Gauge that measures the golden mean with exact proportions of the face. The results of these ratios would also be more accurate if measured in person. However, due to the short time and the resources that are not provided in this investigation, the measurements of the pictures by a ruler are the most accurate data that can be achieved.

In this next chart, the voting popularity throughout the most recent elections will be displayed:

1st election

2nd election

3rd election

4th election

### Justin Trudeau

39.47%

41.5%

38.4%

52.0%

Shinzō Abe

26.73%

27.62%

28.14%

33.11%

Jacob Zuma

69.69%

65.90%

65.90%

62.15%

Sebastián Piñera

44.05%

51.61%

36%

54%

The averages of the facial ratios are shown below:

Trudeau:

((16/13) + (30/21) + (30/18) + (2/1.5))/4 = 1.415

Abe:

((14/10) + (21/19) + (21/18) + (2/2))/4 = 1.168

Zuma:

((9/5) + (28/23) + (28/17) + (3/2))/4 = 1.541

Piñera:

((7/6) + (19/15) + (19/12) + (1.6/1))/4 = 1.404

According to these calculations, Zuma is the most beautiful out of all these leaders, because the average of his proportions are closer to the golden mean (1.618) than any of the other leaders.

The averages of the percentages in each leader can be shown below:

Trudeau:

(39.47 + 41.5 + 38.4 + 52)/4 = 42.84

Abe:

(26.73 + 27.62 + 28.14 + 33.11)/4 = 28.9

Zuma:

(69.69 + 65.9 + 65.9 + 62.15)/4 = 65.91

Piñera:

(44.05 + 51.61 + 36 + 54)/4 = 46.42

According to these calculations, Zuma is the most popular out of all the leaders, because the average of his popularity percentage was greater than any of the other leaders.

These calculations make sense, and provide evidence that beauty does in fact matter in elections. However, can you determine beauty from an equation? By graphing each average percentage popularity votes as the x-values of a coordinate, and each proportion to the corresponding leader as the y-values of a coordinate, I graphed a scatter plot to show correlation and draw a line of best fit. I used the average percentage points to have a constant for each leader because the dependent variable in this investigation is beauty, and how it affects percentage votes in elections, which would be our independent variable:

Eyes: Edge of the Face: (Purple)

y-values (Proportions in the face)

42.84

16:13

28.9

14:10

65.91

9:5

46.42

7:6

Mouth: Nose: (Blue)

y-values (Proportions in the face)

42.84

30:21

28.9

21:19

65.91

28:23

46.42

19:15

Mouth: Side of the Face: (Red)

y-values (Proportions in the face)

42.84

30:18

28.9

21:18

65.91

28:19

46.42

19:12

Front Left Tooth: 2nd Left Tooth: (Black)

y-values (Proportions in the face)

42.84

2:1.5

28.9

2:2

65.91

3:2

46.42

1.6:1

I then plugged each of these coordinate points on a graph, using Desmos computer application, showing each proportion in a different color stated above:

By observation, I can see that these points have a positive correlation, however I had trouble what model it functioned, so I plugged my coordinates into a list, and on my TI-84 Plus calculator, and calculated a linear regression, a natural log regression, an exponential regression, and a power regression. I then plugged in one of my y-values for each equation and whichever equation gave me the closest value to the corresponding x-value was the most accurate line of best fit.

Linear:

y = 0.0084212208x + 0.98382262

(65.91",1.5)

1.5 = 0.0084212208x + 0.98382262

2.48382262 = 0.0084212208x

294.948046 = x

Natural Log:

y = -0.1430837453 + 0.3999082665(ln(x))

(65.91",1.5)

1.5 = -0.1430837453 + 0.3999082665(ln(x))

1.643083745 = 0.3999082665(ln(x))

4.108651616 = ln(x)

60.86459335 = x

Exponential:

y = 1.015111779(1.006285264x)

(65.91",1.5)

1.5 = 1.015111779(1.006285264x)

1.477669781 = 1.006285264x

ln(1.477669781) = xln(1.006285264)

0.3904663747 = 0.0062655941x

62.319130023 = x

Power:

y = 0.435962702(x0.299324518)

(65.91",1.5)

1.5 = 0.435962702(x0.299324518)

3.440661307 = x0.299324518

62.06448976 = x

According to my calculations, the exponential regression is the most accurate line of best fit. I found this by plugging in a specific point on each calculated regression and determining which equation gave me the most accurate answer. In doing this, I determined that beauty in fact does influence political popularity, and I also found an equation that when facial/beauty ratios are put into the y-value, an estimated popularity will be the solution for the x-value.

Conclusion

During this investigation, I have concluded that beauty does in fact matter during elections within a country, regardless of nationality and cultural identity, and I have modeled an exponential function to determine a person’s beauty ratio (y-value) by replacing the x-value with the percentage votes in the elections, or conversely, determine their percentage votes if they were to enter an election (x-value) by replacing the y-value with a person's ratio. This can be used in determining the outcome and rise in power of political leaders, could be used to predict patterns and trends in political science, and potentially help the overall process of elections.

Obviously, there may be faults in this equation, as it is the line of best fit, and there are always outliers in a set of data, meaning an extremely attractive person may lose an election due to scandals, or inexperience, while an extremely unattractive person may win the election because of trustworthiness and experience for the job. These extraneous variables are impossible to quantify, especially since there are no physical numbers for trustworthiness or the extent of a scandal. What I have attempted to do in this investigation is present clear and concise math to determine a constant trend in a subject that is not only interesting, but that is applicable to all parts of the world. This is a subject of importance because politics is ubiquitous—from the bankers on Wall Street, to the peasants of China—and with this sabermetric approach to politics, it will lead us into the future of leadership.

### Bibliography

“Electoral History of Justin Trudeau.” Wikipedia, Wikimedia Foundation, 18 Apr. 2018",

en.m.wikipedia.org/wiki/Electoral_history_of_Justin_Trudeau.

“Shinzō Abe.” Wikipedia, Wikimedia Foundation, 23 Jan. 2019",

en.m.wikipedia.org/wiki/Shinz%C5%8D_Abe.

“Jacob Zuma.” Wikipedia, Wikimedia Foundation, 27 Jan. 2019",

en.m.wikipedia.org/wiki/Jacob_Zuma.

“Sebastián Piñera.” Wikipedia, Wikimedia Foundation, 26 Jan. 2019",

en.m.wikipedia.org/wiki/Sebasti%C3%A1n_Pi%C3%B1era.

“Explore Math with Desmos.” Desmos Graphing Calculator, www.desmos.com/.