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Modelling Opinion Dynamics in the Age of Algorithmic Personalisation

Nicola Perra, Luis E C Rocha

arXiv:1811.03341v1physics.soc-phcs.SI

TL;DR

Algorithmic personalization filters information to address the mismatch between abundant content and limited attention, while its effects on opinion formation remain poorly understood. The paper models networked users updating opinions from selected posts and examines filtering methods, network structures, and nudging. Filtering interacts with network correlations to shape polarization and echo chambers, while nudging can move population opinion toward the pushed view.

  • Problem

    Algorithmic gatekeeping’s effects on opinion formation are poorly understood, despite platforms filtering information to address information overload and limited attention.

    Source: Introduction · pp. 1–2

  • Method

    The paper models networked users updating opinions from filtered timelines and compares time-, preference-, and random-based selection, network structures, and centrally nudged opinions.

    Source: Introduction · p. 2, Network Structure · p. 3, Algorithmic Personalisation and… · p. 4

  • Results

    Filtering interacts with network correlations to produce polarization and echo chambers; semantic filtering reinforces a predominant opinion under unbalanced starts, while nudging can move opinion toward the pushed view and eventually switch the status quo.

    Source: Discussion · p. 10

  • Takeaways & Limitations

    Opinion dynamics can be manipulated by personalization, while correlated social ties are associated with polarization and echo chambers and heterogeneous contacts can hinder compact domains.

    Source: Discussion · p. 10

    The model omits users unfollowing friends with diverging opinions, a form of manual curation that might further contribute to opinion bubbles and bias toward users’ own opinions.

    Source: Discussion · p. 10

Abstract

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Modern technology has drastically changed the way we interact and consume information. For example, online social platforms allow for seamless communication exchanges at an unprecedented scale. However, we are still bounded by cognitive and temporal constraints. Our attention is limited and extremely valuable. Algorithmic personalisation has become a standard approach to tackle the information overload problem. As result, the exposure to our friends' opinions and our perception about important issues might be distorted. However, the effects of algorithmic gatekeeping on our hyper-connected society are poorly understood. Here, we devise an opinion dynamics model where individuals are connected through a social network and adopt opinions as function of the view points they are exposed to. We apply various filtering algorithms that select the opinions shown to users i) at random ii) considering time ordering or iii) their current beliefs. Furthermore, we investigate the interplay between such mechanisms and crucial features of real networks. We found that algorithmic filtering might influence opinions' share and distributions, especially in case information is biased towards the current opinion of each user. These effects are reinforced in networks featuring topological and spatial correlations where echo chambers and polarisation emerge. Conversely, heterogeneity in connectivity patterns reduces such tendency. We consider also a scenario where one opinion, through nudging, is centrally pushed to all users. Interestingly, even minimal nudging is able to change the status quo moving it towards the desired view point. Our findings suggest that simple filtering algorithms might be powerful tools to regulate opinion dynamics taking place on social networks

Introduction

Social platforms use algorithmic curation to manage information competing for limited attention, but its societal effects remain poorly understood. The paper studies how personalization methods shape opinion dynamics across network settings.

Introduction

  • Social interactions spread information and shape opinion formation, with both the authority and number of contacts affecting individuals’ opinions.Social influence also appears in marketing, politics, and health interventions.Source: Introduction · p. 1
  • Social platforms help users manage information competing for limited attention, while the societal effects of algorithmic curation remain uncertain.Online interaction increases the speed and diversity of information exchange, but users remain subject to cognitive and temporal constraints.Source: Introduction · p. 1
  • Platforms order and filter information using popularity, semantic similarity, and collaborative recommendations based on what similar or connected users consume.Personalization draws on explicit user-provided information and implicit signals from prior interactions and content.Source: Introduction · p. 2
  • Algorithmic gatekeeping’s short- and long-term societal effects remain unclear, making the design of optimal solutions difficult and potentially counterintuitive.Debate includes concerns about filter bubbles, reduced serendipity, technical bias, sensitive-data access, and tensions between commercial and societal objectives, alongside arguments that personalization helps manage information overload.Source: Introduction · p. 2
  • The study models networked users who share and update opinions, examining filtering by time ordering or prior expressed opinions and centrally pushed nudges.The effects are studied across different initial conditions and network topologies.Source: Introduction · p. 2

Materials and Methods

The paper models two-opinion dynamics in a social network where users see only selected posts from friends. It compares random, time-based, preference-based, and nudged timelines while accounting for network structure, activation, and filtering.

Materials and Methods

  • Users choose between opinions A and B according to the proportions of each shown in their timelines, while only some information shared by friends is displayed.The model compares random selection, time-based ordering, ordering by users’ previously expressed ideological leanings, and a centrally chosen opinion inserted into timelines.Source: Materials and Methods · pp. 2–3
  • The model combines the social network, an activation mechanism governing when information is exchanged, and a filter selecting which posts appear in each timeline.The three components are shown in Fig. S1.Source: Materials and Methods · p. 3
  • The model extends prior work by studying opinion dynamics and multiple sorting algorithms in a network of interacting users, rather than meme spread or a single user and news aggregator.Prior models discussed also include item or purchase choices, which the authors distinguish from the opinion processes studied here.Source: Materials and Methods · p. 3

Network Structure

The study compares networks that vary in degree heterogeneity, clustering, path length, and spatial structure to examine how topology interacts with filtering.

Network Structure

  • The configuration model has a heterogeneous power-law degree distribution, while Watts–Strogatz variants and a regular lattice provide homogeneous-degree comparisons.The configuration model uses P(k) ∝ k^-2.5 with k_min = 2 and average degree 5.5; the Watts–Strogatz model begins with degree 6 and varies rewiring probability.Source: Network Structure · p. 3
  • Watts–Strogatz rewiring distinguishes high-clustering networks with long or short paths from a low-clustering, short-path random network.The study uses g = 0, 10^-2, and 1 to create these configurations.Source: Network Structure · p. 3
  • The regular lattice has degree four, zero clustering, and long average path length due to spatial clustering between nodes.Simulations use N = 10^5 and average over 10 independent network realizations, except for the non-random lattice.Source: Network Structure · p. 3

Nodes Activation

Users activate probabilistically, broadcast their current opinion, and then update it based on the opinions visible in their timelines. The main setting uses heterogeneous activation probabilities, with a homogeneous-probability comparison reported as qualitatively similar.

Nodes Activation

  • When active, a user broadcasts their opinion to friends and updates their own according to the shares of opinions in their timeline.A timeline showing 30% opinion A and 70% opinion B yields respective adoption probabilities of 0.3 and 0.7.Source: Nodes Activation · pp. 3–4
  • Main-text simulations draw activation probabilities from a power-law distribution over p ∈ [0.01, 1].The model uses heterogeneous activation because analyses of real online networks show heterogeneous propensity to initiate social interaction.Source: Nodes Activation · p. 4
  • With constant activation probability p = 0.1, the supplemental analyses produce results qualitatively similar to the heterogeneous-activation case.The value 0.1 is the average activation probability in the heterogeneous case.Source: Nodes Activation · p. 4

Algorithmic Personalisation and Filtering

Users accumulate opinions shared by friends between activations, then a filtering method selects up to Q items to form the timeline that informs them.

Algorithmic Personalisation and Filtering

  • Li(t) contains opinions posted by friends since the user’s last activation, plus opinions in the user’s timeline at that time.The list is the pool from which the next timeline is formed.Source: Algorithmic Personalisation and… · p. 4
  • REF samples Q items randomly; OLD and REC prioritize older and newer posts, respectively, while PR sorts posts by the user’s current opinion.NU replaces a random fraction z of opinions with a centrally chosen opinion.Source: Algorithmic Personalisation and… · p. 4
  • Each method forms a timeline of at most Q items from Li(t), and the remaining items are discarded.The main text uses Q = 20; the passage says this value has little impact on results.Source: Algorithmic Personalisation and… · p. 4

Results

The section examines how ranking methods affect group and individual opinion dynamics, then investigates centrally controlled nudging.

Results

  • The section first studies REF, OLD, REC, and PR for their effects on group and individual opinion dynamics.Source: Results · p. 4
  • It then investigates nudging as a form of centrally controlled bias.Source: Results · p. 4
  • The section’s scope is the effect of sorting algorithms and centrally controlled bias on opinion dynamics.Source: Results · p. 4

Opinion dynamics subject to algorithmic personalisation

Filtering’s effects on opinion prevalence and neighborhood structure depend on starting shares and network topology: preference-based sorting can reduce minority opinion, while correlations can foster polarization and echo chambers.

Opinion dynamics subject to algorithmic personalisation

  • The model schematic shows how friends’ posts accumulate in Li and how each algorithm selects the first Q posts to inform the active user.The illustrated example sets Q = 3.Source: Figure S1 · p. 5
  • PR’s minority decline occurs mainly in the first 200 steps; PA(500) is 0.06 in WS g=1, 0.08 in CM, and 0.09 in the other three networks.The passage attributes weaker reductions in heterogeneous networks to hubs that limit the algorithm’s ability to hide the subordinate opinion.Source: Opinion dynamics subject to… · p. 5
  • Under equal starts, highly clustered networks show strong polarization; PR produces only low polarization in WS g=1, and heterogeneous CM does not show those small clusters.Source: Opinion dynamics subject to… · p. 5
  • With equal shares, all four methods preserve prevalence; from 20:80 starts, PR lowers minority A while REF, OLD, and REC preserve the status quo.Source: Opinion dynamics subject to… · pp. 4–5, Figure S2 · p. 6
  • Topological and spatial correlations can create compact echo chambers even when total opinion shares remain stable; heterogeneous contact patterns somewhat hinder their formation.Source: Opinion dynamics subject to… · p. 6
  • From unbalanced starts, PR reduces A’s visibility and share, while OLD and other sorting methods produce relatively more subordinate-opinion echo chambers in WS g=1 than in CM.Source: Opinion dynamics subject to… · p. 6
  • With unbalanced starts, high-clustering networks have two orders of magnitude more A echo chambers than initially, while spatial correlations produce effects of about a factor of six.The passage says these correlations interact with sorting to create compact domains that boost survival of the less common opinion relative to the other two networks.Source: Opinion dynamics subject to… · p. 6
  • Figure S3 tracks the distribution of each user’s fraction of nearest neighbors holding opinion A at t=500, normalized against t=0 across ten bins.Source: Opinion dynamics subject to… · p. 5, Figure S3 · p. 7

Nudging Scenario

With 10% of timeline opinions centrally replaced by A, the population moves toward A across starting conditions, networks, and sorting algorithms. Random selection reaches A fastest, while older-post sorting is slowest and correlations can shield users from nudging.

Nudging Scenario

  • Across all networks and sorting algorithms, replacing 10% of shown opinions with A moves group opinion toward A, often making A dominant by about 100–150 steps from unbalanced starts.By t = 500, almost the entire population has adopted A.Source: Nudging Scenario · p. 7
  • REF reaches convergence fastest across topologies, whereas OLD is slowest; at z = 0.05, PR is generally between OLD and the faster methods.For z ≥ 0.15, REF, REC, and PR convergence times become weak functions of z and initial opinion shares.Source: Nudging Scenario · p. 7
  • At z = 0.05, PR slows convergence especially on clustered WS and spatial LA networks, where echo chambers shield users from the nudged opinion.The convergence-time simulations cap T* at 10^4, so curves reaching that limit have actual convergence times above it.Source: Nudging Scenario · p. 7
  • At t = 500, neighborhood distributions are skewed toward all-A neighborhoods, while heterogeneous connectivity hampers echo-chamber formation compared with WS networks at g = 1.The plotted distribution is the fraction of each node’s friends sharing its opinion, normalized against t = 0.Source: Nudging Scenario · p. 8, Figure S6 · p. 9

Discussion

The discussion argues that filtering and network structure jointly shape opinion dynamics, with correlations associated with polarization and echo chambers. It also notes model limitations, including omitted unfollowing, resistance to opinion change, and simplified networks and filters.

Discussion

  • With balanced initial shares, filtering leaves overall opinion shares unchanged, but clustering and spatial correlations can form like-minded domains, while heterogeneous contacts hamper echo chambers.With unbalanced shares, semantic filtering further increases the predominant opinion, although correlations can protect subordinate-opinion domains.Source: Discussion · pp. 9–10
  • Under central nudging, the population can switch toward the desired opinion; random and recent-post filtering speed convergence, while older posts slow it.When only one timeline post is manipulated, PR can slow convergence in topologically or spatially correlated networks, where echo chambers oppose the shift.Source: Discussion · p. 10
  • The authors warn that algorithmic personalization can manipulate opinion dynamics, while the feedback between filtering and network structure remains complex and understudied.They note that exposure to opposing viewpoints may itself increase polarization.Source: Discussion · p. 10
  • The model omits unfollowing, resistance to change, unequal friend authority, and more realistic filters; it also studies only prototypical network models.Future work could model adaptive, time-varying ties and networks with communities, higher-order correlations, or temporal connectivity.Source: Discussion · p. 10

Supplemental Information for “Modeling opinion dynamics in the age of algorithmic polarization”.

The supplement describes the filtering and opinion-update model and presents sensitivity analyses. It specifies how timelines are curated and how users adopt an opinion from the posts they see.

Supplemental Information for “Modeling opinion dynamics in the age of algorithmic polarization”.

  • The supplement covers filtering methods, the opinion-dynamics model, and sensitivity analyses of main-parameter variation.It also examines constant activation rates, different timeline sizes, and more unbalanced initial conditions.Source: Supplemental Information for “Modeling… · p. 13

A. Algorithmic Personalization Mechanisms

  • Each active node assembles friends’ posts and its existing timeline, then a filter selects up to Q posts: random REF, newest REC, oldest OLD, or current-opinion-biased PR.Posts exceeding the timeline limit are removed; PR preferentially presents posts matching the user’s current opinion.Source: A. Algorithmic Personalization… · p. 13

B. Opinion Dynamics Model

  • After filtering, a user adopts opinion A or B with probability equal to that opinion’s fraction of posts in the curated timeline.The update is probabilistic, so either opinion may be adopted when its timeline share is nonzero.Source: B. Opinion Dynamics Model · p. 13

C. Sensitivity Analysis

The sensitivity analysis tests alternative activation rates, timeline sizes, and initial opinion shares. With constant activation rates, its reported patterns remain broadly consistent with the main-text results, including the roles of semantic filtering and network structure.

C. Sensitivity Analysis

  • The sensitivity analysis also examines different Q sizes and more unbalanced initial conditions, in addition to constant activation rates.Source: C. Sensitivity Analysis · p. 13

1. Constant activation rates

  • With constant activation p = 0.1, balanced starts retain the status quo, while PR reduces the subordinate opinion from unbalanced starts, most strongly on WS networks with g = 1.High clustering and heterogeneous connectivity hamper that reduction.Source: §1 · pp. 13–14, Figure S7 · p. 14
  • For balanced starts, clustered WS networks induce polarization, especially under PR; for unbalanced starts, PR forms echo chambers around the dominant opinion across network types.Heterogeneous connectivity hampers this tendency, and the reported patterns are in line with those for heterogeneous activity.Source: §1 · p. 14

D. Different queue sizes

Queue-size variations preserve broad patterns, while small queues alter polarization on highly clustered networks. Under more extreme initial imbalance, the subordinate opinion persists, though semantic filtering reduces it and network structure weakens that reduction.

D. Different queue sizes

  • At Q=5, REF and REC produce more polarization than PR in highly clustered WS networks, although results are otherwise qualitatively similar across Q.When Q is below the WS average degree of 6, PR can reduce polarization; with Q=1, any same-opinion neighbor prevents a node from switching.Source: D. Different queue sizes · p. 14, Figure S9 · p. 15
  • With 20–80 initial conditions, topological and spatial correlations create echo chambers around the subordinate opinion, with stronger effects under REC and REF.Source: D. Different queue sizes · p. 14, Figure S10 · p. 16
  • At Q=5, semantic filtering remains the only sorting mechanism reducing the subordinate opinion; clustering, spatial correlation, and degree heterogeneity weaken that reduction versus WS g=1.These network features hamper the reduction less than they do at Q=20.Source: D. Different queue sizes · p. 15, Figure S11 · p. 16

E. 1 −99 and 10 −90 initial conditions

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