Modelling the Closed Loop Dynamics Between a Social Media Recommender System and Users' Opinions

TL;DR

The paper addresses how a social media recommender system and users’ opinions coevolve in a closed-loop setting. It introduces a mathematical framework combining a time-varying bipartite graph, Friedkin–Johnsen style opinion dynamics, and a softmax-based RS driven by engagement, watch time, and virality, with memory. Through extensive Monte Carlo simulations, it analyzes how the softmax parameter $\alpha$, content diversity $k$, virality weighting $\omega$, and memory $\delta$ shape engagement, polarisation, and radicalisation, revealing that initial opinion distributions critically influence outcomes and that viral neutral content can dampen polarisation. The findings offer actionable insights for RS design to mitigate polarisation, such as moderating exploration, maintaining content diversity, and leveraging virality for neutral content, with implications for platform policy and algorithmic governance.

Abstract

This paper proposes a mathematical model to study the coupled dynamics of a Recommender System (RS) algorithm and content consumers (users). The model posits that a large population of users, each with an opinion, consumes personalised content recommended by the RS. The RS can select from a range of content to recommend, based on users' past engagement, while users can engage with the content (like, watch), and in doing so, users' opinions evolve. This occurs repeatedly to capture the endless content available for user consumption on social media. We employ a campaign of Monte Carlo simulations to study how recommender systems influence users' opinions, and in turn how users' opinions shape the subsequent recommended content. Both the performance of the RS (e.g., how users engage with the content) and the polarisation and radicalisation of users' opinions are of interest. We find that different opinion distributions are more susceptible to becoming polarised than others, many content stances are ineffective in changing user opinions, and creating viral content is an effective measure in combating polarisation of opinions. This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible.

Figures (16)

• Figure 1: A schematic showing the components of the model (users, content, RS) as a closed-loop system. Here, the example consists of four users ($n=4$), and three pieces of content ($k=3$). At each timestep, user $i$ receives a piece of content $z_i(t)$ from the RS, with stance $x_{z_i(t)}$. The user watches the content for a time $w_{iz_i(t)}(t)$, according to Eq. (\ref{['eq:watch_rate']}), and engages with the content, according to Eq. (\ref{['eq:log_linear_like']}). Watching this content causes user $i$'s opinion $x_i(t)$ to evolve via Eq. (\ref{['eq:user_opinion']}). The user's engagement decision, $y_i^j(t)$, and their watch rate, $w_{ij}(t)$ are then relayed back the RS and used to update user-specific and content-specific variables $A_i^j(t)$, $B_i^j(t)$ and $C^j(t)$. These variables are used to better tailor the next recommendation, $z_i(t+1)$ according to Eq. (\ref{['eq:softmax_func']}), closing the loop.
• Figure 2: The two initial opinion distributions, $x_i(0)$, used throughout simulations.
• Figure 3: Example simulations showing the total likes per piece of content, the opinion distributions, and the content recommendations over time for $\alpha=14$ (Panels (a), (b), and (c)) and for $\alpha = 18$ (Panels (d), (e), and (f). In more detail, (a) and (d) show the total likes from the entire population, per piece of content. Panels (b) and (e) show the initial opinion distribution compared to the final opinion distribution, highlighting the effect of the RS on the population opinions. Finally, (c) and (f) show a contour plot representing all content recommended to each user (indexed on the $y$-axis) over time.
• Figure 4: Research Question One, in (a) the performance metrics of the RS; $\mathrm{Likes\,\%}$, Eq. (\ref{['eq:likes']}), and $\mathrm{Average\,Watch\,Rate\,\%}$ (WR), Eq. (\ref{['eq:avg_watch_rate']}), are shown for different values of the softmax parameter, $\alpha$. In (b), the final percentage changes of the polarisation metric $M_D(\tau)$, Eq. (\ref{['eq:dispersion']}), and radicalisation metric $M_R(\tau)$, Eq. (\ref{['eq:radicalisation']}), are plotted for different values of $\alpha$.
• Figure 5: Research Question Two, in (a) the performance metrics of the RS; $\mathrm{Likes\,\%}$, Eq. (\ref{['eq:likes']}), and $\mathrm{Average\,Watch\,Rate\,\%}$ (WR), Eq. (\ref{['eq:avg_watch_rate']}), are shown for different number different of content, $k$. In (b), the final percentage changes of the polarisation metric $M_D(\tau)$, Eq. (\ref{['eq:dispersion']}), and radicalisation metric $M_R(\tau)$, Eq. (\ref{['eq:radicalisation']}), are plotted for different values of $k$.