The Mathematical phenomenon that makes you feel like you're (still) not popular.
In math, there is a bizarre concept that points out something you've known since high school: your friends are more popular than you are.
In episode 43 of Game Theory, Nick and Chris break down the math of why your friends are -- factually -- more popular than you are.
From Episode 42 of Game Theory:
Listen to episode 31 wherever podcasts are found.
The Math
The idea was first observed back in 1991 by a mathematician named Scott L. Feld back in 1991. The paradox is two-fold:
People are factually more likely to be friends with people who have more friends than they do.
People believe they have more friends than their friends do.
That means that you are more likely to be less popular than your friends, but you probably think you're more popular than them.
This, of course, makes no sense on the surface. If every single person on the planet is only friends with people more popular than them, we would run out of people. There has to be a most- and least-popular person on the planet.
Well, that's the paradox. This highlights something in statistics called sampling bias which creates an illusion. But, it does exist.
You can check out the mathematical explanation for yourself on Wikipedia.
But, the basic reason this phenomenon is observable, is because of something called centrality. This is a complicated mathematic principle in its own right but means that there will be a most popular friend in each group -- a queen bee if you will.
The graphic below illustrates this better than I could write it.
As you can see, I think, there is a central node. And that person isn't friends with everyone in the group, but they are friends with most people who also have large networks.
A good way to think about them is by using a term we've all come to know in the post--COVID-19 ere: superspreader.
The usefulness of this observation is profound, and something we've been in need of in recent years -- vaccination policy.
By understanding the complexity of (in-person) social networks, scientists can more accurately understand the best ways to roll out a vaccine to provide the most safety.
The friendship paradox is also relevant in election forecasting. By polling individuals you think are the most popular in a friend group, you can get more data than if you simply choose a random person and hope they are the central figure in the group.
Whether it be vaccine policy or election forecasting, you want to find the central nodes within networks.
Human Choice
The issue -- and why we at Game Theory are interested in this -- is that humans are not predictable machines. We are complicated, growing, evolving, sentient beings. This means that we can gain friends, lose friends, change social circles, etc.
This exact aspect of game theory has been exemplified by both the COVID-19 pandemic and the 2016 and 2020 elections.
In 2016, Democratic Nominee Hillary Clinton appeared to be a heavy favorite but lost the general election handily to Republican Nominee Donald Trump.
Check out this much better explanation here:
One reason the pollsters were so shocked was that, while they'd sampled the correct centralized nodes in social circles, many of those who were planning to vote for eventual President Trump, chose either not to participate in the poll or to purposefully mislead pollsters.
As a result, the centralized nodes were useless in forecasting the election.
Similarly, governments -- mostly the U.S. and Canada -- struggled to compel a necessary percentage of the population to receive COVID-19 vaccination, making it irrelevant who the central nodes were in friend groups.
The use of the friendship paradox makes me uncomfortable as it continues the march toward turning all human beings into a collection of data. But, it's hard to argue with the usefulness of understanding sampling bias and centrality among social networks.
But, you always have a choice.
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