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Can Users Fix Algorithms? A Game-Theoretic Analysis of Collective Content Amplification in Recommender Systems

Ekaterina Fedorova, Madeline Kitch, Chara Podimata

TL;DR

The paper studies how users may collectively influence recommender systems by strategically interacting with content, modeling the RecSys as a collaborative-filtering problem and introducing a one-round low-rank abstraction to analyze welfare. It derives sufficient conditions under which a majority-led collective uprating a minority item can Pareto-improve recommendations and social welfare, and provides a robust algorithm to compute effective uprating values. Empirically, the framework is validated on Goodreads data and via a user survey, showing that collectives can improve minority content promotion with limited impact on overall accuracy and even benefit platform engagement under certain utility functions. The work has design and policy implications, suggesting that algorithmic protest may sometimes align with platform incentives and that mechanisms could be designed to harness or mitigate such collective behavior depending on objectives. Overall, it advances the understanding of multi-agent strategic dynamics in RecSys and offers practical tools for evaluating and guiding collective actions in content recommendation ecosystems.

Abstract

Users of social media platforms based on recommendation systems (e.g. TikTok, X, YouTube) strategically interact with platform content to influence future recommendations. On some such platforms, users have been documented to form large-scale grassroots movements encouraging others to purposefully interact with algorithmically suppressed content in order to counteractively ``boost'' its recommendation. However, despite widespread documentation of this phenomenon, there is little theoretical work analyzing its impact on the platform or users themselves. We study a game between users and a RecSys, where users (potentially strategically) interact with the content available to them, and the RecSys -- limited by preference learning ability -- provides each user her approximately most-preferred item. We compare recommendations and social welfare when users interact with content according to their personal interests and when a collective of users intentionally interacts with an otherwise suppressed item. We provide sufficient conditions to ensure a pareto improvement in recommendations and strict increases in user social welfare under collective interaction, and provide a robust algorithm to find an effective collective strategy. Interestingly, despite the intended algorithmic protest of these movements, we show that for commonly assumed recommender utility functions, effective collective strategies also improve the utility of the RecSys. Our theoretical analysis is complemented by empirical results of effective collective interaction strategies on the GoodReads dataset and an online survey on how real-world users attempt to influence others' recommendations on RecSys platforms. Our findings examine how and when platforms' recommendation algorithms may incentivize users to collectivize and interact with content in algorithmic protest as well as what this collectivization means for the platform.

Can Users Fix Algorithms? A Game-Theoretic Analysis of Collective Content Amplification in Recommender Systems

TL;DR

The paper studies how users may collectively influence recommender systems by strategically interacting with content, modeling the RecSys as a collaborative-filtering problem and introducing a one-round low-rank abstraction to analyze welfare. It derives sufficient conditions under which a majority-led collective uprating a minority item can Pareto-improve recommendations and social welfare, and provides a robust algorithm to compute effective uprating values. Empirically, the framework is validated on Goodreads data and via a user survey, showing that collectives can improve minority content promotion with limited impact on overall accuracy and even benefit platform engagement under certain utility functions. The work has design and policy implications, suggesting that algorithmic protest may sometimes align with platform incentives and that mechanisms could be designed to harness or mitigate such collective behavior depending on objectives. Overall, it advances the understanding of multi-agent strategic dynamics in RecSys and offers practical tools for evaluating and guiding collective actions in content recommendation ecosystems.

Abstract

Users of social media platforms based on recommendation systems (e.g. TikTok, X, YouTube) strategically interact with platform content to influence future recommendations. On some such platforms, users have been documented to form large-scale grassroots movements encouraging others to purposefully interact with algorithmically suppressed content in order to counteractively ``boost'' its recommendation. However, despite widespread documentation of this phenomenon, there is little theoretical work analyzing its impact on the platform or users themselves. We study a game between users and a RecSys, where users (potentially strategically) interact with the content available to them, and the RecSys -- limited by preference learning ability -- provides each user her approximately most-preferred item. We compare recommendations and social welfare when users interact with content according to their personal interests and when a collective of users intentionally interacts with an otherwise suppressed item. We provide sufficient conditions to ensure a pareto improvement in recommendations and strict increases in user social welfare under collective interaction, and provide a robust algorithm to find an effective collective strategy. Interestingly, despite the intended algorithmic protest of these movements, we show that for commonly assumed recommender utility functions, effective collective strategies also improve the utility of the RecSys. Our theoretical analysis is complemented by empirical results of effective collective interaction strategies on the GoodReads dataset and an online survey on how real-world users attempt to influence others' recommendations on RecSys platforms. Our findings examine how and when platforms' recommendation algorithms may incentivize users to collectivize and interact with content in algorithmic protest as well as what this collectivization means for the platform.

Paper Structure

This paper contains 76 sections, 34 theorems, 133 equations, 3 figures, 8 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Our Contributions
  3. Related works
  4. Model & Preliminaries
  5. Background: Online Matrix Completion
  6. Abstraction
  7. Model summary
  8. Learner's protocol (Protocol \ref{['prot:learner']})
  9. Users' agency
  10. When are collectives effective?
  11. Poor minority recommendation without strategic interactions
  12. Improving recommendations via simple collective rating strategies
  13. Collective uprating
  14. Algorithms to find effective collective strategies
  15. Algorithm \ref{['alg:find_eta_aglo']} robustness
  16. ...and 61 more sections

Key Result

Proposition 2.1

Assume that $\bf{R}^\star$ satisfies Definition def:majority-minority-matrix, and that for any $(u,i) \in \Omega$ s.t. $u \in \mathcal{U}_\textsc{min}$ and $i \in \mathcal{I}_\textsc{min}$, $r^\star_{u,i} = 0$. Then, the sparsest $\widehat{\mathbf{R}}$ solving Equation eqn:rank_min is such that $\ha

Figures (3)

  • Figure 1: [In]correct recommendation of books by their author popularity, measured by $\#$ of total interactions an author gets. Books shelved by fewer than $5$ users are dropped. More popularity metrics in \ref{['app:experiment_additional_results']}.
  • Figure 2: [In]correct recommendation of books by their author popularity, measured by how often the author is added to shelf. Books shelved by fewer than $5$ users are dropped.
  • Figure 3: [In]correct recommendation of books by their popularity, measured by how often they are added to shelf. Books shelved by fewer than $5$ users are dropped.

Theorems & Definitions (108)

  • Definition 1: Observed pairs, $\Omega$
  • Definition 2: Majority-minority matrix
  • Proposition 2.1: Estimated Minority Item Ratings are Zero
  • Definition 3
  • Definition 4: $\alpha$-loss tolerant learner
  • Proposition 2.2
  • Theorem 3.1: Truthfulness is good for majority, bad for minority
  • Definition 5: Picky Users
  • Definition 6: $(\eta, \mathcal{U}_\textsc{coll})$-Sufficient Singular Value Gap
  • Theorem 3.2: Improving Recommendations
  • ...and 98 more