A meritocratic network formation model for the rise of social media influencers

Abstract

Many of today’s most used online social networks such as Instagram, YouTube, Twitter, or Twitch are based on User-Generated Content (UGC). Thanks to the integrated search engines, users of these platforms can discover and follow their peers based on the UGC and its quality. Here, we propose an untouched meritocratic approach for directed network formation, inspired by empirical evidence on Twitter data: actors continuously search for the best UGC provider. We theoretically and numerically analyze the network equilibria properties under different meeting probabilities: while featuring common real-world networks properties, e.g., scaling law or small-world effect, our model predicts that the expected in-degree follows a Zipf’s law with respect to the quality ranking. Notably, the results are robust against the effect of recommendation systems mimicked through preferential attachment based meeting approaches. Our theoretical results are empirically validated against large data sets collected from Twitch, a fast-growing platform for online gamers.

Individual Fairness for Social Media Influencers

“…Focusing on this alternative approach, one line of research in sociology (Stochastic Actor Oriented Models [15]) and one in economics (strategic network formation models [16]) take an utilitarian perspective: agents build their connections to maximize some benefit e.g., their network centrality. The quality-based model of Pagan et al [4] combines these approaches by using a UR or PA-based RSs and a utilitarian following decision-making function for users. To enhance our understanding on the coupling between RS and human network behavior, we add a non-exploratory RS and investigate the fairness of the resulting outcomes.…”

“…Design-wise, there is an ongoing struggle to develop diverse RSs [7][8][9] which, moreover, ensure that any two items could be recommended jointly to users [10]. This perhaps explains why the popularity-based algorithms implemented within the RS community [12,21] differ from PA [4,14] by not allowing for a complete exploration of alternatives. Our motivation to analyse extreme PA is grounded in this prior work, although our goal is to understand the network-formation process and its fairness.…”

“…As mentioned in the previous two sections, our work is based on the qualitybased model proposed by [4] and briefly presented below. As any model, this is based on some simplifying assumptions, for which we refer the user back to the original paper.…”

“…To first understand the structure and the properties of these social media platforms, [4] proposed a simple model in which (a) each CC has an intrinsic and objective quality, (b) in each round, users receive a recommendation for a CC (which could be drawn from the uniform distribution, or from a preferential attachment (PA) process), and (c) users follow the recommended CC if this CC has a higher quality than all the user's current followees. By simulating this model, Pagan et al [4] showed that the expected number of followers (in-degree) of the CCs follow a Zipf's law [5]. In particular, the expected rankings of CCs given by their quality and by the number of followers are the same.…”

“…However, such ex-ante fairness does not imply ex-post fairness (i.e., even if in expectation CCs receive a number of followers proportional to their quality, many of the actual outcomes that could materialize are unfair) [11]. Moreover, as also noted by the authors [4], there might be long times to convergence. This means that even if a fair outcome would eventually be reached, this might not happen within reasonable time.…”