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335 – Statistics: The Secret Weapon of Web Giants

Friendship Paradoxes and the Quora Downvoting Paradox

at Quora, Inc.

The "friendship paradox" refers to the statistical pattern that, for most participants in many social networks, their friends have more friends on average than they do. In recent years, the availability of large volumes of data on online social networks has enabled the study of the friendship paradox in new contexts and on unprecedented scales. Researchers have shown that phenomena similar to the friendship paradox, called "generalized friendship paradoxes," occur in quantities other than friend count: for example, in certain online social networks, the average neighbor of a typical individual is a more active user and content contributor. Furthermore, researchers have also found that online social networks exhibit stronger friendship and generalized friendship paradoxes than are usually measured in the literature: often, for most people in a social network, most of their neighbors score more highly on various metrics. This is typically a stronger statement than the usual one about mean of the quantity over neighbors. In this article, we apply these developments in the study of the friendship paradox to Quora, an online knowledge-sharing platform. There is a directed social network of people following one another on Quora, and we first confirm that standard directed- network variants of the friendship paradox occur in this context. We then proceed to investigate a more exotic variant of the friendship paradox that we call "downvoting paradox." This is a variant of the phenomenon that emerges through one of the core interactions on Quora, the "downvote," which people use to give negative feedback on one another's answers. Under certain conditions on the contribution level of the participants, we find that, for most people who got downvoted in a given period of time, most of their downvoters got downvoted more than they did. This is an example of a paradox occurring in a network that represents negative interactions, which is a relatively unexplored context. Furthermore, certain aspects of the product mechanics of Quora make this a particularly interesting setting to explore these types of phenomena. We discuss the implications of the observation of the "downvoting paradox" and suggest opportunities for further investigation.