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The Feedback Loop Between Recommendation Systems and Reactive Users

Atefeh Mollabagher, Parinaz Naghizadeh

TL;DR

This work studies the closed-loop between recommender platforms and reactive users who can opt out of engaging with recommended content. It develops a formal model where a user's opinion $x_k\in[-1,1]$ evolves under platform recommendations $u_k\in[-1,1]$, with a binary click indicator, and where both platform and user maximize respective utilities over a horizon $K$. The authors introduce three agent policies (fixed, decreasing, adaptive decreasing) and two platform policies (fixed recommendations, explore periodically), and derive finite-time and asymptotic characterizations of opinion dynamics: under fixed recommendations the opinion drifts toward $u_0$ with limit $\eta x_0 + (1-\eta) u_0$, under decreasing policies the drift is eliminated or limited, and under adaptive decreasing it remains within a bounded drift around the innate opinion $x_0$. They prove that reactive policies can prevent or restrict undesirable opinion shifts and that, depending on parameters, adaptive decreasing can yield higher long-run utility than fixed strategies. Numerical experiments validate these insights and illustrate macroscopic effects on population opinion distributions and platform payoffs, as well as the impact of exploration on transient dynamics. The work highlights practical implications for user strategy design and platform regulation, offering a framework to balance engagement with resistance to opinion drift.

Abstract

Recommendation systems underlie a variety of online platforms. These recommendation systems and their users form a feedback loop, wherein the former aims to maximize user engagement through personalization and the promotion of popular content, while the recommendations shape users' opinions or behaviors, potentially influencing future recommendations. These dynamics have been shown to lead to shifts in users' opinions. In this paper, we ask whether reactive users, who are cognizant of the influence of the content they consume, can prevent such changes by actively choosing whether to engage with recommended content. We first model the feedback loop between reactive users' opinion dynamics and a recommendation system. We study these dynamics under three different policies - fixed content consumption (a passive policy), and decreasing or adaptive decreasing content consumption (reactive policies). We analytically show how reactive policies can help users effectively prevent or restrict undesirable opinion shifts, while still deriving utility from consuming content on the platform. We validate and illustrate our theoretical findings through numerical experiments.

The Feedback Loop Between Recommendation Systems and Reactive Users

TL;DR

This work studies the closed-loop between recommender platforms and reactive users who can opt out of engaging with recommended content. It develops a formal model where a user's opinion evolves under platform recommendations , with a binary click indicator, and where both platform and user maximize respective utilities over a horizon . The authors introduce three agent policies (fixed, decreasing, adaptive decreasing) and two platform policies (fixed recommendations, explore periodically), and derive finite-time and asymptotic characterizations of opinion dynamics: under fixed recommendations the opinion drifts toward with limit , under decreasing policies the drift is eliminated or limited, and under adaptive decreasing it remains within a bounded drift around the innate opinion . They prove that reactive policies can prevent or restrict undesirable opinion shifts and that, depending on parameters, adaptive decreasing can yield higher long-run utility than fixed strategies. Numerical experiments validate these insights and illustrate macroscopic effects on population opinion distributions and platform payoffs, as well as the impact of exploration on transient dynamics. The work highlights practical implications for user strategy design and platform regulation, offering a framework to balance engagement with resistance to opinion drift.

Abstract

Recommendation systems underlie a variety of online platforms. These recommendation systems and their users form a feedback loop, wherein the former aims to maximize user engagement through personalization and the promotion of popular content, while the recommendations shape users' opinions or behaviors, potentially influencing future recommendations. These dynamics have been shown to lead to shifts in users' opinions. In this paper, we ask whether reactive users, who are cognizant of the influence of the content they consume, can prevent such changes by actively choosing whether to engage with recommended content. We first model the feedback loop between reactive users' opinion dynamics and a recommendation system. We study these dynamics under three different policies - fixed content consumption (a passive policy), and decreasing or adaptive decreasing content consumption (reactive policies). We analytically show how reactive policies can help users effectively prevent or restrict undesirable opinion shifts, while still deriving utility from consuming content on the platform. We validate and illustrate our theoretical findings through numerical experiments.

Paper Structure

This paper contains 20 sections, 4 theorems, 10 equations, 8 figures, 3 algorithms.

Table of Contents

  1. Introduction
  2. Model
  3. Agent's model
  4. Platform's model
  5. Platform's and Agent's Policies
  6. Platform's Policies
  7. Agent's Policies
  8. Analysis
  9. Numerical Experiments
  10. Fixed recommendations
  11. Macroscopic changes
  12. Exploring recommendations
  13. Conclusion
  14. Detailed Expressions of Weights in Proposition \ref{['prop:single-opinion']}
  15. Second appendix
  16. ...and 5 more sections

Key Result

Proposition 1

Consider an agent with innate opinion $x_0 \in [-1,1]$ who receives the recommendation $u_0 \in [-1,1]$. Let $x_{i}^{(p)}$ be the agent's opinion at the beginning of block $i$ when following policy $p \in \{1,2,3\}$, from Algorithms alg:policy-one, alg:policy-two, and alg:policy-three, respectively. where $\Upsilon_{i}^{(p)}$ (resp. $\Gamma_{i}^{(p)}:=1-\Upsilon_{i}^{(p)}$) is the influence of the

Figures (8)

  • Figure 1: The feedback loop between a recommendation platform and agents. Without the red arrows, the model captures feedback loops with passive agents (studied in prior works). Our model (with the red arrows included) captures feedback loops with reactive agents, whose actions are informed by both the recommendation $u_{k-1}$ and their latest opinion $x_{k-1}$.
  • Figure 2: Possible length of clicking periods in Policy \ref{['alg:policy-three']}.
  • Figure 3: Agent's opinion and utility, platform's utility, and final opinion distribution under different agent policies and fixed platform recommendations.
  • Figure 4: Agent's opinion and utility, and platform's utility, under different agent policies and varying platform recommendations.
  • Figure 5: Impact of varying $\alpha$ on the agent's final opinion, agent's final utility, and platform's final utility
  • ...and 3 more figures

Theorems & Definitions (6)

  • Proposition 1
  • Proposition 2
  • Corollary 1
  • Proposition 3
  • proof
  • proof