Your friends are statistically likely to have more friends than you.

你的朋友在統計上很可能比你有更多朋友。

Sounds funny but it's an actual phenomenon called the 'friendship paradox'.

聽起來有趣，但這實際上是一個稱為「友誼悖論」的現象。

It's a paradox that doesn't only apply to friendships, but also to other areas of your life such as dating, social media, sports and pretty much most things that can be described as a social network.

這個悖論不僅適用於友誼，還適用於生活中的其他領域，比如約會、社交媒體、體育和幾乎所有可以描述為社交網絡的事物。

We're going to be looking at how this paradox affects your life and why it's good to be aware of it.

我們將看看這個悖論如何影響你的生活，以及為什麼了解它很重要。

I also asked my audience to participate in an experiment.

我還邀請我的觀眾參加一個實驗。

I analyzed the Twitter accounts of 89 of my subscribers to find out if their followers have more followers than them and to see if the friendship paradox applies.

我分析了89位訂閱者的Twitter帳戶，以找出他們的粉絲是否比他們有更多的追隨，並查看友誼悖論是否適用。

But before we dive into that, let's try to understand: how does this paradox work?

但在深入探討之前，讓我們試著了解：這個悖論是如何運作的呢？

If our friends have more friends than us then the paradox can't possibly be true for them as well, right?

如果我們的朋友比我們有更多的朋友，那麼這個悖論對他們來說也不可能成立，對吧？

Let's imagine a classroom with 9 students. 

讓我們想像一個有9名學生的教室。

Let's assume everyone has 2 friends.

假設每個人都有 2 個朋友

In this scenario, the friendship paradox is not true for anyone right now.

假設每個人都有2個朋友。

Everyone's friends also have two friends each.

在這種情況下，友誼悖論現在對任何人都不成立。

However, in almost every social network, there are people with more connections than others.

每個人的朋友也都有兩個朋友。

Let's add a tenth person who's a bit more popular than his colleagues.

然而，在幾乎所有的社交網絡中，都有比其他人更多連接的人。

He's friends with six people. Let's see what that does to the network.

讓我們加一個比他的同事更受歡迎的第十個人。

Let's start with the people on the sides who are not connected to him

他有六個朋友。讓我們看看這對網絡有什麼影響。

The people on the edges continue having two friends, 

讓我們從那些與他沒有聯繫的兩邊的人開始。

but now those friends have three friends each, since they are now connected to the popular guy.

邊緣的人繼續有兩個朋友，但現在每個人有三個朋友，因為他們現在與這位受歡迎的人有聯繫。

So the friendship paradox is now true for this case.

所以友誼悖論現在對這種情況成立。

The people in the middle now have 3 friends, but those friends have an average of 3.7 friends.

中間的人現在有3個朋友，但這些朋友平均有3.7個朋友。

That's because they're now friends with the popular guy who skews the average up.

那是因為他們現在是這位受歡迎的人的朋友，這使平均值偏高。

So the friendship paradox is also true for the people in the middle.

所以友誼悖論也適用於中間的人。

The only one who is not affected by the friendship paradox is the popular guy, who has way more friends than his friends.

唯一不受友誼悖論影響的是那位受歡迎的人，他的朋友比他的朋友多得多。

In this scenario, the friendship paradox is true for 90% of the classroom.

在這種情況下，友誼悖論對教室中90%的人都成立。

It's actually a simple phenomenon if you think about it:

實際上，如果你仔細思考，這是一個簡單的現象：

Popular people are friends with many people.

受歡迎的人有很多朋友。

Therefore, they are more likely to be your friends and they skew the average up.

因此，他們更有可能成為你的朋友，並使平均值偏高。

Social networks often have a small group of people with many connections.

社交網絡通常有一小群人有許多連接。

This phenomenon is actually quite common in other real-world networks as well.

這種現象實際上在其他現實世界的網絡中也很常見。

Networks are often concentrated around certain points, or nodes, the technical term, that have more connections than the remaining nodes.

網絡通常集中在某些具有比其餘節點更多連接的特定點或節點，技術術語稱之為「節點」。

For example, this affects online networks.

例如，這影響了線上網絡。

There's a Facebook dataset collected by Stanford with data from 4000 volunteers.

斯坦福收集的一份Facebook數據集，其中包含了來自4000名志願者的數據。

If we look at this data, we see that 87% of those people have fewer Facebook friends than their Facebook friends.

如果我們查看這些數據，我們會發現87%的人在Facebook上擁有的朋友少於他們的Facebook朋友。

The friendship paradox is also visible in transportation networks.

友誼悖論也在運輸網絡中可見。

If we look at the Eurail train network, we see that each city is connected to 2.7 cities on average whereas their neighboors are connected to 3.8 cities.

如果我們查看歐鐵列車網絡，我們會發現每個城市平均連接到2.7個城市，而他們的鄰居連接到3.8個城市。

There's a group of central stations which have more connections than their neighboors and are responsible for most of the traffic.

有一組中央車站，它們比鄰居擁有更多的連接，並負責大部分交通。

Notice how most of them are European capitals.

請注意，其中大多數是歐洲首都。

This phenomenon is also relevant to understand how diseases spread.

這種現象還與理解疾病的傳播有關。

People with more social connections are more likely to catch and spread infections.

具有更多社交聯繫的人更有可能感染和傳播疾病。

So, how does this affect your life?

那麼，這如何影響你的生活？

In dating, it's more likely that your partners have had more partners than you.

在約會方面，你的伴侶更有可能比你有更多的伴侶。

In my previous video, I made a simulation of a dating app.

在我的上一影片頻中，我製作了一個約會應用程序的模擬。

In this simulation, 78% of users who got matches matched with people that had more matches than them.

在這個模擬中，78%的用戶與擁有比他們更多配對的人相匹配。

When you play Call of Duty or Fifa online and you get trashed by someone, there's a good chance that on the other side, there's a person who plays more often and against more people than you.

當你在線上玩《決勝時刻》或《FIFA》並被某人擊敗時，有很大的可能性，在另一邊有一個比你更常玩，對抗更多人的人。

When you go to the gym, it's more likely that the people you find there go to the gym more often than you.

當你去健身房時，你遇到的人更有可能比你經常去健身房。

Therefore, it's normal if they are in better shape than you.

因此，如果他們比你身材更好，那是正常的。

Even though the friendship paradox is easy to understand, it's not always intuitive and it's a common bias.

儘管友誼悖論很容易理解，但它並不總是直觀的，而且是一種常見的偏見。

We would think that our friends are a fairy representative sample of typical people, but that's not always true.

我們通常會認為我們的朋友是典型人的一個相對代表性樣本，但這並不總是真實的。

In this case, they have more friends than the typical person.

在這種情況下，他們的朋友比典型人多。

In statistics, this is called a sampling bias:

在統計學中，這稱為抽樣偏差：

When our sample of data points is biased in a way that does not represent the entire population.

當我們的數據點樣本出現偏差，不代表整個人口。

That's why we should be careful when we make generalizations from the things we see.

這就是為什麼我們在從我們看到的事物中做一般性概括時應該小心。

We often understand reality through social networks. We follow newspapers, influencers and friends.

我們經常通過社交網絡來理解現實。我們關注報紙、影響者和朋友。

We might think they give us an accurate image of the world, but they can also suffer from a sampling bias.

我們可能認為它們給我們提供了世界的準確形象，但它們也可能受到抽樣偏差的影響。

Today's sponsor tries to remove the sampling bias from your news.

今天的贊助商試圖消除你在新聞中的抽樣偏差。

Ground News is a website and app that allows you to see how the same story is told by left, center and right sources.

Ground News 是一個網站和應用程序，可以讓你查看左派、中間和右派來源如何報導同一故事。

For example, if you want to learn more about how Elon Musk restricted satellite service to Ukraine,

例如，如果你想了解有關Elon Musk限制對烏克蘭的衛星服務的報導，

you can see if most of the sources reporting this news lean left or right, and you can see how it was reported by each side.

你可以查看大多數報導這則消息的來源是左派還是右派，以及每一方如何報導這一消息。

So in this case, some left leaning sources emphasize the fact that Elon Musk interfered with Ukraine whereas right leaning sources put more emphasis on the fact that he prevented an attack.

因此，在這種情況下，一些左派來源強調Elon Musk干涉烏克蘭的事實，而右派來源更加強調他阻止了一次攻擊。

They have a feature called blindspot that shows you stories that are disproportionately covered by one side of the political spectrum.

他們有一個名為盲點的功能，它顯示那些被政治譜系的一側過分報導的故事。

They also have a phone app and you can get a personalized feed based on your interests.

他們還有一個手機應用程序，你可以根據自己的興趣獲得個人化的信息源。

The amount of bias in news is one of the reasons why I use data to tell my stories and one of the reasons why I created this channel in the first place.

新聞中的偏見程度是我使用數據來講述故事的原因之一，也是我創建此頻道的首要原因之一。

Personally, I think it's very healthy to look at the perspective from opposite views, 

我個人認為，從相反觀點的角度看問題是非常有益的，

even if it makes us feel uncomfortable, and I love what Ground News is doing here.

即使這讓我們感到不舒服，我喜歡 Ground News 在這方面所做的工作。

They even have a feature called My News Bias, which is a dashboard for your news consumption.

他們甚至有一個名為My News Bias的功能，就是的新聞消費儀表板。

It's only available through their Vantage plan and if you subscribe through my link, you get 30% off and it would be a big support to my channel.

它只能通過他們的Vantage計劃獲得，如果你通過我的連結訂閱，可以享受30％的折扣，這將對我的頻道提供重要支持。

Now let's see the results of our Twitter experiment.

現在讓我們看看我們Twitter實驗的結果。

I asked my audience to share their Twitter usernames.

我要求我的觀眾分享他們的Twitter用戶名。

The goal here is to find their number of followers, and then compare that with the number of followers of the followers to see if the friendship paradox is true for them.

這裡的目標是找到他們的粉絲數，然後將其與他們的粉絲的粉絲數進行比較，以查看友誼悖論是否適用於他們。

I also gave the participants the option to remain anonymous, so some of them will have nicknames.

我還給參與者提供了匿名的選擇，所以其中一些人將使用綽號。

89 people participated in the survey.

共有89人參加了調查。

Of these people, seven provided non-existent usernames so I excluded them.

中有七人提供了不存在的用戶名，因此我將他們排除在外。

One person claimed to be Elon Musk, so I decided to exclude them as well.

還有一個人聲稱是伊隆·馬斯克，所以我決定將他們排除在外。

Elon, if it's really you watching my videos then I'm sorry, but I can't afford to analyze all your followers.

如果伊隆，如果你真的在看我的影片，那麼對不起，但我無法負擔分析你所有的粉絲。

The next step was to get the number of followers for everyone.

接下來的步驟是獲取每個用戶的追隨者數。

I signed up for Twitter's API and after some work I got the follower count per user.

我註冊了Twitter的API，經過一些工作後，我得到了每個用戶的追隨者數。

Three people had private accounts so I was not able to look into their list of followers.

有三個人是不公開的帳號，所以我無法查看他們的追蹤者列表。

Sorry, I forgot to mention that in the survey.

對不起，我忘記在調查中提到這一點。

Eight people had zero followers, so I had to exclude them as well.

還有八個人一個追蹤都沒有，所以我不得不將他們排除在外。

Sorry, but I can't check if the friendship paradox applies to you if you don't have friends in the first place.

對不起，但如果你一開始就沒有朋友，我無法檢查友誼悖論是否適用於你。

The next step was to find the list of followers for every user.

接下來的步驟是查找每個用戶的追蹤者列表。

To my disappointment, I found out that Twitter recently disabled the API's endpoint I needed to do this.

令我失望的是，我發現Twitter最近禁用了我需要的API端點。

But after some research, I found a third party website that provides this service and I got the lists of followers.

但經過一些研究，我找到了一個提供此服務的第三方網站，並獲得了追蹤者列表。

The final results: There were only two participants that had more followers than their followers.

最終結果：只有兩位參與者的追蹤者比他們的追蹤者多。

For the remaining 97% of participants, the friendship paradox was true: their followers had more followers than them.

對於其餘的參與者，即97％，友誼悖論是成立的：他們的追蹤者比他們的追蹤者多。

So, in conclusion, if the people around you have more connections then you don't feel bad because that's quite normal according to math.

因此，總之，如果你周圍的人有更多的連接，那麼根據數學來看，你不必感到不安。

And personally, I would be careful when making a generalization out of the people around you.

對於周圍的人做一個概括時，我個人會謹慎一些。

There's a good chance you're facing a sampling bias and that the people connected to you don't represent the entire network.

很有可能你面臨的是抽樣偏差，與你相連的人不代表整個網絡。

Thank you for watching. If you like stories told with data and would like to support my work, consider leaving a like and subscribing to the channel.

謝謝觀看。如果你喜歡通過數據講述的故事，並希望支持我的工作，請考慮點贊和訂閱我的頻道。

And thank you to our patrons.

感謝我們的贊助者。