> This comes about because the distribution of friends on social networks follows a power law. So while most people will have a small number of friends, a few individuals have huge numbers of friends. And these people skew the average.
> Here’s an analogy. If you measure the height of all your male friends. you’ll find that the average is about 170 centimeters. If you are male, on average, your friends will be about the same height as you are. Indeed, the mathematical notion of “average” is a good way to capture the nature of this data.
> But imagine that one of your friends was much taller than you—say, one kilometer or 10 kilometers tall. This person would dramatically skew the average, which would make your friends taller than you, on average. In this case, the “average” is a poor way to capture this data set.
Based on the wikipedia article of the friendship paradox[1], the power law distribution really has nothing to do with it, and the paradox would exist even if the distribution of number of friends were completely uniform. It's instead related to the fact that people with a high number of friends are overrepresented in the lists of other peoples' friends. The rest of the author's analysis describing the new "paradox" passes the smell test, however.
Some nodes have more connections than others. If most of these nodes send out a signal, it will seem to the other nodes that the majority of ALL nodes sent the signal, even if the highly-connected nodes are actually a minority.
e.g. if the popular kids believe X, then to most people it will seem like the majority believe X, even if there are only a few popular kids.
Say there are 100 people on a social network: 50 with tons of friends ("popular"), and 50 with only a couple of friends ("unpopular").
If you pick a random person out of the social network's user list, there's an equal probability they'll be popular or unpopular. But if you start from your friend list and pick a random user from there, it's more likely that the person will be popular, because popular people appear on more friend lists.
Now say there's some belief that most of the popular people agree with, but unpopular people don't. ("Popular people are better than other people"? ;)) Everyone decides to post their opinion on this topic on the social network. Because most of your friends are popular, it will look to you as though there's majority agreement, even though the opinions are actually split 50/50.
In real life, the numbers are more extreme. The top percentage can have thousands or tens of thousands of friends. If these users hold an opinion, it can skew people's perceptions a lot more easily.
> Here’s an analogy. If you measure the height of all your male friends. you’ll find that the average is about 170 centimeters. If you are male, on average, your friends will be about the same height as you are. Indeed, the mathematical notion of “average” is a good way to capture the nature of this data.
> But imagine that one of your friends was much taller than you—say, one kilometer or 10 kilometers tall. This person would dramatically skew the average, which would make your friends taller than you, on average. In this case, the “average” is a poor way to capture this data set.
Based on the wikipedia article of the friendship paradox[1], the power law distribution really has nothing to do with it, and the paradox would exist even if the distribution of number of friends were completely uniform. It's instead related to the fact that people with a high number of friends are overrepresented in the lists of other peoples' friends. The rest of the author's analysis describing the new "paradox" passes the smell test, however.
[1] https://en.wikipedia.org/wiki/Friendship_paradox