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Mathematical Framework for Online Social Media Auditing

Wasim Huleihel, Yehonathan Refael

TL;DR

This paper mathematically formalizes this framework and utilizes it to construct a data-driven statistical auditing procedure to regulate AF from deflecting users' beliefs over time, along with sample complexity guarantees.

Abstract

Social media platforms (SMPs) leverage algorithmic filtering (AF) as a means of selecting the content that constitutes a user's feed with the aim of maximizing their rewards. Selectively choosing the contents to be shown on the user's feed may yield a certain extent of influence, either minor or major, on the user's decision-making, compared to what it would have been under a natural/fair content selection. As we have witnessed over the past decade, algorithmic filtering can cause detrimental side effects, ranging from biasing individual decisions to shaping those of society as a whole, for example, diverting users' attention from whether to get the COVID-19 vaccine or inducing the public to choose a presidential candidate. The government's constant attempts to regulate the adverse effects of AF are often complicated, due to bureaucracy, legal affairs, and financial considerations. On the other hand SMPs seek to monitor their own algorithmic activities to avoid being fined for exceeding the allowable threshold. In this paper, we mathematically formalize this framework and utilize it to construct a data-driven statistical auditing procedure to regulate AF from deflecting users' beliefs over time, along with sample complexity guarantees. This state-of-the-art algorithm can be used either by authorities acting as external regulators or by SMPs for self-auditing.

Mathematical Framework for Online Social Media Auditing

TL;DR

This paper mathematically formalizes this framework and utilizes it to construct a data-driven statistical auditing procedure to regulate AF from deflecting users' beliefs over time, along with sample complexity guarantees.

Abstract

Social media platforms (SMPs) leverage algorithmic filtering (AF) as a means of selecting the content that constitutes a user's feed with the aim of maximizing their rewards. Selectively choosing the contents to be shown on the user's feed may yield a certain extent of influence, either minor or major, on the user's decision-making, compared to what it would have been under a natural/fair content selection. As we have witnessed over the past decade, algorithmic filtering can cause detrimental side effects, ranging from biasing individual decisions to shaping those of society as a whole, for example, diverting users' attention from whether to get the COVID-19 vaccine or inducing the public to choose a presidential candidate. The government's constant attempts to regulate the adverse effects of AF are often complicated, due to bureaucracy, legal affairs, and financial considerations. On the other hand SMPs seek to monitor their own algorithmic activities to avoid being fined for exceeding the allowable threshold. In this paper, we mathematically formalize this framework and utilize it to construct a data-driven statistical auditing procedure to regulate AF from deflecting users' beliefs over time, along with sample complexity guarantees. This state-of-the-art algorithm can be used either by authorities acting as external regulators or by SMPs for self-auditing.
Paper Structure (40 sections, 11 theorems, 81 equations, 2 figures, 3 algorithms)

This paper contains 40 sections, 11 theorems, 81 equations, 2 figures, 3 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Main Contributions
  4. Conceptual Contributions
  5. Unifying framework.
  6. Automatic online auditing procedure.
  7. Technical Contributions
  8. Notations
  9. Framework: Setup and Goal
  10. The setup
  11. Reference feeds.
  12. Counterfactual regulation.
  13. Auditor's goal
  14. Average violation.
  15. Testing.
  16. ...and 25 more sections

Key Result

Lemma 3

For any $k,\ell\geq 1$ and irreducible Markov chains $\mathscr{M}$,

Figures (2)

  • Figure 1: An illustration of the interaction between the platform, the user, and the auditor.
  • Figure 2: An illustration of the auditing procedure. The SMP and the uniformal filter get as an input the external data procedure, then output the filtered and the reference feeds, respectively. Both feeds are seen by the auditor, where the last outputs "YES" when the regulation is not violated, or "NO" otherwise.

Theorems & Definitions (15)

  • Remark 1: Worst-case violation
  • Definition 2: $\ell$-joint-$k$-cover time
  • Lemma 3
  • Theorem 4: Sample complexity
  • Theorem 5: Sample complexity
  • Definition 6: Counterfactual total variability
  • Theorem 7: Sample complexity
  • Lemma 8
  • Lemma 9
  • Corollary 10
  • ...and 5 more