Recommender system in X inadvertently profiles ideological positions of users

Paul Bouchaud; Pedro Ramaciotti

Figure 1: Schematic representation of the population of X users for the study and the inference of their position in the embedding space of X’s recommender system. (A) Population of the study (data volunteers

\mathcal{V}

and recommended users

\mathcal{U}

) subtending networks for friend recommendation (in orange arrows) and following relations (in purple arrows), collected respectively with a data donation program using a browser plug-in and X’s API. (B) Schematic representation of the embedding space with every user

i

in the population

\mathcal{E}

having a position

\phi_{i}

in the 256-dimensional embedding.

Figure 2: Characterization of the population in the study. (A) Distribution of Left-Right ideological leaning of X users segmented by age and gender. (B) Pairwise Spearman correlations between the inferred attributes of users (* indicates p-value

<0.01

, ** indicates p-value

<0.001

). The correlation between Left-Right leaning and degree of interest in news is -0.14**. The density plots for the degree of interest in news of users in different age groups illustrates a comparatively higher correlation between this attribute and age.

Figure 3: (A) Three-dimensional representation of directions in the 256-dimensional embedding space of the recommender system that maximize the correlation with attributes of users, identified using Canonical Correlation Analysis (CCA). The three-dimensional visualization was obtained through a Locally Preserving Projection [ 37 ] . Vector norms of directions associated with attributes correspond to absolute correlations with these attributes, reported in the adjacent table (all p-values

<0.0001

). (B) Absolute cosine similarity computed in the 256-dimensional embedding space between directions in the embedding space identified with CCA and that maximize correlations with attributes of users (* indicates p-value

<0.01

). (C) Comparison of attributes of users along the CCA directions in the embedding that maximize correlations with three features: Left-Right leaning

\mathbf{w}_{LR}

, age

\mathbf{w}_{age}

, and gender

\mathbf{w}_{gender}

.

Figure 4: Constraining user recommendations from leveraging left-right political information. (A) Diagram of the intervention procedure. After identifying the direction in the latent space that maximally correlates with users’ left-right political leaning, we iteratively project user representations onto the orthogonal subspace. (B) Effects on recommendations of constraining political information in the embedding of the recommender systems. For each user in the population, we compute 50 friend recommendations before (in blue) and after (in green) the intervention and compute the impact the distribution of the ideological diversity of recommendations as the standard deviation on the Left-Right scale, and the relevance as the similarity in interest in news between recipient of recommendations and recommended friends.

Figure S1 : Diagram (adapted from [ 75 ] ) of Twitter/X “Who to Follow” (WTF) account recommendation system that computes the three friend recommendations that are proposed on the right-hand lateral bar in the website of X. The WTF recommender system can be organized in three main sub-parts: 1) candidate generation (left part of the figure), 2) integration of features computed by machine learning models (at the center of the figure), and 3) candidate mixing and ranking (on the right part of the figure).

Figure S2 : Diagram of the representation of the data used for training the recommender system in X, adapted from [ 22 ] (A) X’s Heterogeneous Information Network (HIN, a graph abstraction model for Knowledge Graph data) showing interconnections between entities that are relevant for recommendation (tweets, users, advertisers, advertisements) through diverse relations (authorship, follows, interactions, shares or clicks). (B) Part of the HIN representation relevant for the inference of the embedding space in our study, including “Follow” and “Who to Follow” relationships between users form a sub-network analyzed in this work.

Figure S3 : Screenshot of the survey presented to volunteers of the data donation program (in French), asking: their gender, age group, their “ideological position” on a 101-point scale with political parties arranged from Left to Right for reference and orientation, whether they connect to Twitter from their phone or their computer or both. The survey also asks the same question for YouTube (not used in this study).

Figure S4 : Evolution of the number of friend recommendations (WTF) seen by volunteers in our study and collected with our browser plug-in. The observation period of the study extended from January 1st, 2023, to May 1st, 2024. The number of collected recommendations depends on the number of volunteers participating in the project, which saw an increase in May 2024 due to the visibility of changes in content moderation and data accessibility brought about by the change in ownership of the platform. We include tests of accuracy and reliability tests in the inference of the embedding space, and that use different temporal windows in sampling, to demonstrate that the inference is robust throughout the whole period of observation.

Figure S5 : (A) Distribution of accounts based on how many volunteers received them as recommendations. (B) Distribution of the number of friends accounts for each user in

\mathcal{E}

.

Twitter Handle	Recommendation Rate	Description
@elonmusk	35.4%	Owner, CTO and Exec. Chairman of Twitter
@BFMTV	30.8%	French News Broadcast Channel
@MrBeast	28.1%	Popular YouTube Content Creator
@EmmanuelMacron	22.3%	President of France (2017-2027)
@GabrielAttal	20.7%	Former Prime Minister of France (2024)

Table S1 : Most recommended accounts seen by our volunteers, with the rate or fraction of volunteers that saw the recommendation during the observation period.

Figure S6 : Distribution of accounts’ degree.

Figure S7 : Analysis of the degree distribution of second-degree neighbors. Distribution (left figure) and Cumulative Distribution (right figure) of the in-degree of second-degree neighbors, with respect to first-degree neighbors, normalized per volunteer by the largest in-degree. The distribution for recommended second-degree neighbors is shown as a dashed red line.

Figure S8 : Accuracy of the trained algorithm and its embedding space in predicting observed data for different training parameters. (Left figure) AUC-ROC scores for “Who to Follow” predictions as a function of

\alpha

, with error bars showing standard deviation across ten replications. (Right figure) AUC-ROC values for “Who to Follow” (in orange ) and “Follow” (in cyan ) predictions versus training epoch

Figure S9 : Demographic and political characterization of volunteers in the study using surveys administered at enrollment via the browser plug-in. Distribution of volunteers’ self-declared demographics (in blue ) and weighted by “Who to Follow” samples collected per volunteer (in red ), including gender, age, and political leaning. “Unknown” category reflects unfilled optional survey fields, 45.9% of volunteers did not disclose a political preference.

Figure S10 : Distribution of X users in our study by attributes related to activity on the platform, on a logarithmic scale, with mean values indicated by dashed red lines and median by dashed blue lines: follower count (top left), friend-to-follower ratio (top right), average daily number of likes (bottom left), and average daily number of posts/statuses (bottom right).

Figure S11 : Comparison of the inference of age and gender for users in the study (using M3 model by Wang et al., [ 87 ] ), with an alternative method of inference, the FairFace model (developed by Karkkainen and Joo [ 46 ] ), for robustness. Gender and age distributions predicted by M3 (in blue ) for 24 425 accounts in

\mathcal{E}

and by FairFace (in red ) for the subset of 10 932 accounts with a single visible profile face. One limitation of our study lies in the fact that users may choose profile names, descriptions, and photos that do not match their demographic groups, choosing, for instance, avatars (e.g., cartoons, historic personalities), obfuscated representations (e.g., disguises, photos where they do not appear clearly), or even misleading representations (e.g., seeking to appear to other users as being from a demographic group other than their own). We argue that this limitation does not impact the main findings of our study, as these occurrences do no affect the overall trend between features in the absence of reason to believe that their frequency should be dependent on the main variables against which we test independence to demographic features: namely, political leaning.

Figure S12 : Confusion matrices comparing the demographic inference achieved by M3 and by FairFace models on users in our study, for gender (left figure) and age (right figure) for 10 932 accounts with visible profile faces in

\mathcal{E}

.

Figure S13 : Distribution of users by percentage of tweets that they produce on each topic, according to the topic classifier from [ 2 ] . Most users produce a low percentage of their tweets on contents that are classifiable into topics from [ 2 ] . The exception is the topic “News % Social Concern”: users are more evenly distributed when organized by the % of tweets their produce in this topic, and slightly bimodal, concentrated around 10% and 90% of tweets in this topic.

Figure S14 : Figure taken from the methodology report of the dataset of politically positioned users from the Twitter French political Twittosphere and that we use in this study [ 65 ] . Users (followers of MPs, density shown in light blue ) are embedded along two political dimensions: Left-Right and an Anti-elite rhetoric dimension. Positions in the dimension are calibrated using data from the Chapel Hill Expert Survey (CHES) [ 43 ] , and that provide positions of parties as reference points in space. Positions of MPs and political parties used in the calibration are shown in colors. Along the Left-Right scale 0 is the left-most position for political parties, while 10 is the right-most, and 5 is the political center. Along the Anti-elite rhetoric scale 0 stands for no salience of anti-establishment and anti-elite rhetoric, while 10 stands for extreme salience of anti-establishment and anti-elite rhetoric.

Figure S15 : Figures taken from the methodological report of the dataset of politically positioned users from the Twitter French political Twittosphere [ 65 ] , reporting the validation of spatial positioning of users along the political dimensions. Density of users labeled as identified with “left”, “right”, “elite”, or “populist” along dimensions Left-Right (left figure) and Anti-elite rhetoric (right figure). Labeling was computed with annotations produced by the LLM Zephyr 7B

\beta

[ 74 ] . The figure shows the goodness of fit of logistic regressions as classifiers of pairs of labels using the political dimension on which they are embedded. Individuals displaying populist discourse (e.g., subscribing to a vision of society divided into the “people” and “elites”) may also be part of elite political or economic groups. The validation proposed by the authors of the dataset [ 65 ] relies on the fact that most individuals that display high anti-elite and anti-establishment views will not be themselves part of the elite, and that if the proposed validation metrics hold, it will be despite the fact there may be some elite individuals displaying anti-elite and/or anti-establishment rhetoric.

Figure S16 : Comparison of positions along the two political dimensions for the population available from the data from [ 65 ] , and the intersection of 8 249 users in the population

\mathcal{E}

of our study (31.1%). Distribution of users Left-Right (left figure) leaning and Anti-Elite rhetoric (right figure) within the embedded population

\mathcal{E}

(in red ) compared to the distribution within the overall French Twitter population (in blue ) from the dataset of politically-positioned Twitter users from [ 65 ] .

Figure S17 : Validation of the positions of 8 249 users in the population

\mathcal{E}

of our study (31.1%) that are also in dataset from [ 65 ] , by checking that labeled users are also correctly ordered by the two political dimensions. Distribution of users Left-Right leaning (left figure) and Anti-Elite rhetoric (right figure) within the embedded population

\mathcal{E}

segmenting those labeled either as “ Left ” or “ Right ”, and either as “ Elite ” or “ Populist ” by a LLM Zephyr 7B

\beta

[ 74 ] .

Figure S18 : Summary of the main attributes of users in our population. Distribution of inferred age and binary gender for the embedded population

\mathcal{E}

(left figure), Scatter plot of embedded users’ positions on the left-right and anti-elite rhetoric scales (right figure).

Figure S19 : Positioning of users by the recommender along direction

\mathbf{w}_{LR}

and validation. (top figure) Scatter plot showing users’ Left-Right political leaning against their projection onto

\mathbf{w}_{LR}

, the embedding direction maximizing feature correlation;

\rho=.887

,

p<10^{-4}

. (bottom figure) Average fraction of followed Members of Parliament from main Left-leaning (LFI), Center (LREM), and Right-leaning (RN) parties, as a function of users’ projection onto

\mathbf{w}_{LR}

.

Figure S20 : Positioning of users by the recommender along direction

\mathbf{w}_{AntiElite}

and validation. (Top) Scatter plot showing users’ Anti-Elite Salience against their projection onto

\mathbf{w}_{AntiElite}

, the embedding direction maximizing feature correlation;

\rho=.863

,

p<10^{-4}

. (Bottom) Average fraction of followed Members of Parliament from Left-leaning (LFI), Center (LREM), and Right-leaning (RN) parties, as a function of users’ projection onto

\mathbf{w}_{LR}

.

Figure S21 : Positioning of users by the recommender along direction

\mathbf{w}_{gender}

and validation. (Top figure) Distribution of inferred-male/female users according to their projection onto

\mathbf{w}_{gender}

. (Bottom figure) Fraction of users following at least one of the popular accounts , as function of their projection onto

\mathbf{w}_{gender}

.

Figure S22 : Positioning of users by the recommender along direction

\mathbf{w}_{age}

and validation. (Top figure) Distribution of users projection onto

\mathbf{w}_{age}

. (Bottom figure) Fraction of users following at least one of the age-popular accounts, as function of their projection onto

\mathbf{w}_{age}

.

Figure S23 : Positioning of users by the recommender along direction

\mathbf{w}_{News}

and validation. (Top figure) Scatter plot of user projections onto embedding direction

\mathbf{w}_{News}

versus their fraction of news-related tweets. (Bottom figure) Fraction of users following at least one account popular among news enthusiasts.

Figure S24 : Positioning of users by the recommender along direction

\mathbf{w}_{Sports}

and validation. (Top figure) Scatter plot of user projections onto embedding direction

\mathbf{w}_{Sports}

versus their fraction of sports-related tweets. (Bottom figure) Fraction of users following at least one account popular among sports enthusiasts.

Figure S25 : Positioning of users by the recommender along direction

\mathbf{w}_{SciencesTech}

and validation. (Top figure) Scatter plot of user projections onto embedding direction

\mathbf{w}_{SciencesTech}

versus their fraction of sciences-and-technology-related tweets. (Bottom figure) Fraction of users following at least one account popular among sciences and technology enthusiasts.

Figure S26 : Positioning of users by the recommender along direction

\mathbf{w}_{complexity}

and validation. (Top figure) Scatter plot showing users’ Lexical Complexity against their projection onto

\mathbf{w}_{complexity}

, the embedding direction maximizing feature correlation;

\rho=.704

,

p<10^{-4}

. (Bottom figure) Fraction of users following at least one of the low-complexity/high-complexity -popular accounts, as function of their projection onto

\mathbf{w}_{complexity}

.

Attributes	Correlation	Attributes	Correlation
Left-Right Leaning	0.89	Interest in Diaries & Daily Life	0.63
Anti-Elite Rhetoric	0.86	Verified Status	0.62
Interest in News & Social Concern	0.85	Interest in Music	0.60
Interest in Sports	0.80	Age	0.56
Interest in Learning & Education	0.76	Interest in Travel & Adventure	0.54
Interest in Science & Technology	0.75	Interest in Other Hobbies	0.53

Table S2 : Pearson correlations induced by CCA directions in the embedding space of the recommender for different attributes of users. CCA directions are those that maximize the correlation between the attributes and the projection of users in the direction. All p-value are

<10^{-4}

.

Figure S27 : Spearman correlation between projection of users in the study onto the CCA directions of the embedding corresponding to different attributes of users. (* indicates p-value

<0.01

, **

<0.001

)

Figure S28 : Scatter plot of user features versus projections onto embedding directions that maximally correlate with user characteristics: number of followers, friend-to-follower ratio, mean daily posts, and mean daily likes (percentile rank).

Figure S29 : Spearman correlation between projection of users in the study onto the CCA directions of the embedding corresponding to different attributes of users. (* indicates p-value

<0.01

, **

<0.001

)

Figure S30 : Scatter plots between projection of users in the study onto the CCA directions of the embedding corresponding to Left-Right leaning

\mathbf{w}_{LR}

, gender,

\mathbf{w}_{gender}

and age

\mathbf{w}_{age}

. Low correlation values show the degree of independence of these attributes as learned by the recommender system.

Figure S31 : Distribution of political diversity in profile recommendations induced by original unprotected embeddings

\Phi

(in green) and protected embeddings

\Phi^{\prime}

(in orange), segmented by users’ Left-Right leaning. Average values are displayed.

Figure S32 : Distribution of gender and age in the population served with the recommendations of listed accounts under the original and political-protected embeddings.

Figure S33 : Drop in AUC-ROC in the prediction of “Who To Follow” edges via the protected embedding as a function of the protected user attributes.

Recommender system in X inadvertently profiles ideological positions of users

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