j_bertolotti,
@j_bertolotti@mathstodon.xyz avatar

There are many situations in the real world where small initial differences can easily grow into very large differences just out of pure chance.
Since we are on a social network, let's create a toy model* where a number of posts all have the same probability to be reposted/shared/boosted by any person seeing them. Since the more people see a post, the more people have a chance of boosting it, the posts with more visibility are also the ones that are likely to gain more visibility. So small initial fluctuations (just one or two extra boosts at the beginning) can lead a post to skyrocket in popularity, even though it is not intrinsically "better" than any of the other.
If we simulate this process numerically and make a histogram of the result, we see that the distribution of how many boosts a post had rapidly grows a tail, with most posts having no visibility whatsoever, and a few having a LOT more than the average.

  • In the jargon, a "toy model" is a very simple (often unrealistic) model, which nevertheless capture the essence of the problem, without being burdened by all the real world complications. If you ever heard about spherical cows in vacuum, that is a toy model!

Animated gif with two plots, side by side. On the left plot a large number of orange dots starts from the bottom, and gradually rise, with a few rising much faster than the other. On the right plot is a histogram of the data showed on the left, that starts as a narrow distribution and then expands into having a long tail.

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