Probably most people you know are more social than you

You might observe:

1. Most of the people I know are more social than me.

And then you might beat up on yourself, concluding:

2. I am less social than most people.

But the inference from (1) to (2) is obviously fallacious.

For whether you know a person is a function of how social you are and how social they are. Thus, the sample of people in (1) suffers from an evident sampling bias: it is skewed towards people who are more likely to be social.

How strong is this bias? Well, here is a model. There are N people. Each person has a sociality score between 0 and 1. Each person knows themselves. For each pair of distinct people, we independently decide if they know each other, with a probability equal to the average of their sociality scores. Then we calculate the fraction of people who have the property that most people they know have a higher sociality score.

Computer simulation gives us about 59% for N = 1000 or N = 1500 with sociality scores uniformly distributed from 0 to 1. I haven’t bothered to come up with a closed form solution.

So the bias isn’t that strong, but indeed most people are such that most people they know are more social than they are.

I just saw this more thorough related study.