Mathematical Modelling of a Ranking Algorithm: The Case of the Social Network VKontakte

Ranking systems play a crucial role in shaping the online information landscape. These black-box algorithms utilize observable information on users' preferences and passions and recommend new friends/followees to users, sort out contents in users' news feeds, or even hint users what political opinions they have at the moment. Despite their importance in understanding the dynamics of social processes in the online domain, we still know very little about their organization. This paper attempts to fill this gap in the scientific knowledge and identifies a very specific ranking algorithm - the algorithm that sorts out comments under posts on social network VKontakte, a Russian popular online media platform. To this end, we located the set of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$N=1000$</tex> posts dedicated to the coronavirus pandemic topic between 12 December 2020 and 1 March 2021, and then downloaded comments attached to them. Besides this, for <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$n=50$</tex> of these posts, we manually retrieved the order in which the comments appear in users' news feeds subject to the ranking algorithm being in charge. Using these data, we study the structure of the information cascades formed by these comments and organization of the ranking algorithm, trying to model it as a specific relevance function that is linear to the comment popularity metrics - the numbers of likes and replies. To identify the ranking algorithm, we developed a simple model of ranking, according to which comments with higher values of a relevance score should feature a higher priority in the news feed, with the score being a linear function of the popularity metrics. We calibrated this model on a dataset of labeled comments and found that both the popularity factors play a significant role in ranking, but the size of the branch has a slightly greater effect.