Yes, your friends are more successful than you are. On “The Majority Illusion in Social Networks”

Recently, I re-read “The Majority Illusion in Social Networks” (by Lerman, Yan and Wu).

The starting point of this paper is the friendship paradox — a situation when a node in a network has fewer friends that its friends have. The authors expand this paradox to what they call “the majority illusion” — a situation in which a node may observe that the majority of its friends have a particular property, despite the fact that such a property is rare in the entire network.

An illustration of the “majority illusion” paradox. The two networks are identical, except for which three nodes are colored. These are the “active” nodes and the rest are “inactive.” In the network on the left, all “inactive” nodes observe that at least half of their neighbors are “active,” while in the network on the right, no “inactive” node makes this observation.F

Besides pointing out the existence of majority illusion phenomenon, the authors used synthetic networks to characterize the situations in which this phenomenon is most prevalent.

 

Quoting the authors:

the paradox is stronger in networks in which the better-connected nodes are active, and also in networks with a heterogeneous degree distribution. […] The paradox is strongest in networks where low degree nodes have the tendency to connect to high degree nodes. […] Activating the high degree nodes in such networks biases the local observations of many nodes, which in turn impacts collective phenomena

The conditions listed in the quote above describe a lot of known social networks. The last sentence in that quote is of a special interest. It explains the contagious nature of many actions, from sharing a meme to buying a new car.

 

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