Friendship Paradox

friendship paradox

The friendship paradox is the phenomenon first observed by the sociologist Scott L. Feld in 1991 that most people have fewer friends than their friends have, on average. It can be explained as a form of sampling bias (e.g. non-random sample) in which people with greater numbers of friends have an increased likelihood of being observed among one’s own friends. In contradiction to this, most people believe that they have more friends than their friends have.

The same observation can be applied more generally to social networks defined by other relations than friendship: for instance, most people’s sexual partners have (on the average) a greater number of sexual partners than they have. In spite of its apparently paradoxical nature, the phenomenon is real, and can be explained as a consequence of the general mathematical properties of social networks.

Feld goes on to make some more qualitative assumptions about the statistical correlation between the number of friends that two friends have, based on theories of social networks such as assortative mixing (individuals commonly choose to associate with others of similar age, nationality, location, race, income, educational level, religion, or language), and he analyzes what these assumptions imply about the number of people whose friends have more friends than they do. The analysis of the friendship paradox implies that the friends of randomly selected individuals are likely to have higher than average centrality.

This observation has been used as a way to forecast and slow the course of epidemics, by using this random selection process to choose individuals to immunize or monitor for infection while avoiding the need for a complex computation of the centrality of all nodes in the network. One study found that those in the center of their social networks can detect flu outbreaks almost 2 weeks before traditional surveillance measures can. They found that using the Friendship paradox to analyze the health of central friends is ‘an ideal way to predict outbreaks, but detailed information doesn’t exist for most groups, and to produce it would be time-consuming and costly.’

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