Echo Chambers on Social Media Gianmarco De Francisci Morales Principal Researcher • CENTAI Team Lead • Social Algorithmics Team 
 [email protected] SALT 

What Causes Polarization? 

Echo Chambers Metaphor with an intuitive notion Situations in which beliefs are ampli fi ed or reinforced by communication and repetition inside a closed system insulated from rebuttal Do they really exist? Formal de fi nition and measures? Causes and consequences? 

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Geiß et al., "Loopholes in the Echo Chambers", Digital Journalism, 2021. 
 https://doi.org/10.1080/21670811.2021.1873811 

Geiß et al., "Loopholes in the Echo Chambers", Digital Journalism, 2021. 
 https://doi.org/10.1080/21670811.2021.1873811 

Echo Chamber De fi nition Echo = opinion Chamber = network Joint content + network de fi nition Echo chamber = opinion expressed by content users receive from network agrees with what they share with the network Homophily of opinion in the information network 

Research Question How do echo chambers present themselves on social media? 

Production/Consumption Consumption What you receive in your feed What your followees tweet Production What you tweet 

Polarity Score Polarity score of a tweet: 
 ideology of the news domain in the tweet Source: 500 most visited domains on Facebook from Bakshy et al., Science, 2016 

δ-partisanship the fraction of themselves as ose to 1 (0) in- ) bent in their , we refer the a small num- nizations (e.g., rsions of news he distribution Figure 2. nalysis. These pectives: (i) the i) the network Figure 1: Example showing the de￿nition of -partisan users. The dotted red lines are drawn at and 1- . Users on the left of the leftmost dashed red line or right of the rightmost one are -partisan. 

Data being bipartisan, for the w that producing content both sides of the political n the network and content- ommonly used in commu- sources that act as ￿lters propose a model based on generalizes the concept of es to all information types oked at gatekeeping prac- that unlike in traditional gatekeeper on social media. n social media also di￿ers a organizations, due to the able to social media users. users who receive content duce content from a single m one side. To the best of Table 1: Description of the datasets. Topic #Tweets #Users Event guncontrol 19M 7506 Democrat ￿libuster for gun- control reforms (June 12–18, 2016)6 obamacare 39M 8773 Obamacare subsidies pre- served in U.S. supreme court ruling (June 22–29, 2015)7 abortion 34M 3995 Supreme court strikes down Texas abortion restrictions (June 27–July 3, 2016)8 combined 19M 6391 2016 US election result night (Nov 6–12, 2016) large 2.6B 676 996 Tweets from users retweeting a U.S. presidential/vice presi- dential candidate (from [19], 2009–2016) ff 4M 3204 ￿ltering for these hashtags gameofthrones 5M 2159 love 3M 2940 tbt 28M 12 778 foodporn 8M 3904 

0 2 4 6 8 0.00 0.25 0.50 0.75 1.00 Production score density ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 0.2 0.4 0.6 0.8 0.00 0.25 0.50 0.75 1.00 Production score Consumption score group ● ● democrat republican 0.2 0.4 0.6 0.8 0 3 6 9 12 density Consumption score GunControl, Pearson Corr: 0.86 (a) (b) (c) (d) (e) (f) (g) (h) (i) (j) Figure 3: Distribution of production and consumption polarity, for P￿￿￿￿￿￿￿￿ (￿rst row) and N￿￿￿P￿￿￿￿￿￿￿￿ (second row) datasets. The scatter plots display the production (x-axis) and consumption ( -axis) polarities of each user in a dataset. Colors indicate user polarity sign, following [6] (grey = democrat, yellow = republican). The one-dimensional plots along the axes show the distributions of the production and consumption polarities for democrats and republicans. Correlation 

Correlation: Gun Control 0 2 4 6 8 0.00 0.25 0.50 0.75 1.00 Production score density ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 0.2 0.4 0.6 0.8 0.00 0.25 0.50 0.75 1.00 Production score Consumption score group ● ● democrat republican 0.2 0.4 0.6 0.8 0 3 6 9 12 density Consumption score GunControl, Pearson Corr: 0.86 

0.0 1.0 0.2 0.3 0.4 Threshold δ partisan bipartisan (a) 0.0 1.0 0.2 0.3 0.4 Threshold δ partisan bipartisan (b) −0.5 0.5 1.5 0.2 0.3 0.4 Threshold δ partisan bipartisan (c) 0.0 1.0 0.2 0.3 0.4 Threshold δ partisan bipartisan (d) 0.0 1.0 0.2 0.3 0.4 Threshold δ partisan bipartisan (e) Figure 5: Absolute value of the user polarity scores for -partisan and -bipartisan users. 5e−07 2e−06 1e−05 0.2 0.3 0.4 Large Threshold δ partisan bipartisan (a) 2e−05 2e−04 2e−03 0.2 0.3 0.4 Combined Threshold δ partisan bipartisan (b) 2e−05 2e−04 2e−03 0.2 0.3 0.4 Guncontrol Threshold δ partisan bipartisan (c) 1e−05 1e−04 1e−03 0.2 0.3 0.4 Obamacare Threshold δ partisan bipartisan (d) 1e−05 1e−04 1e−03 0.2 0.3 0.4 Abortion Threshold δ partisan bipartisan (e) Figure 6: Pagerank for -partisan and -bipartisan users. ble 3: Comparison between -gatekeeper users and a ran- m sample of normal users. A 3 indicates that the corre- onding property is signi￿cantly higher for gatekeepers Table 4: Accuracy for prediction of users who are pa sans (p) or gatekeepers ( ). (net) indicates network and p ￿le features only, (n-gram) indicates just n-gram featur 0.0 1.0 0.2 0.3 0.4 Threshold δ partisan bipartisan (a) 0.0 1.0 0.2 0.3 0.4 Threshold δ partisan bipartisan (b) −0.5 0.5 1 0.2 0.3 0.4 Threshold δ partisan bipartisan (c) 0.0 1.0 0.2 0.3 0.4 Threshold δ partisan bipartisan (d) 0.0 1.0 0.2 0.3 0.4 Threshold δ partisan bipartisa (e) Figure 5: Absolute value of the user polarity scores for -partisan and -bipartisan users. 5e−07 2e−06 1e−05 0.2 0.3 0.4 Large Threshold δ partisan bipartisan (a) 2e−05 2e−04 2e−03 0.2 0.3 0.4 Combined Threshold δ partisan bipartisan (b) 2e−05 2e−04 2e−03 0.2 0.3 0.4 Guncontrol Threshold δ partisan bipartisan (c) 1e−05 1e−04 1e−03 0.2 0.3 0.4 Obamacare Threshold δ partisan bipartisan (d) 1e−05 1e−04 1e−03 0.2 0.3 0.4 Abortion Threshold δ partisan bipartisa (e) Figure 6: Pagerank for -partisan and -bipartisan users. e 3: Comparison between -gatekeeper users and a ran- sample of normal users. A 3 indicates that the corre- Table 4: Accuracy for prediction of users who are p sans (p) or gatekeepers ( ). (net) indicates network and Price of Bipartisanship: PageRank 

Price of Bipartisanship: PageRank Threshold δ (b) Threshold δ (c) Threshold δ (d) Absolute value of the user polarity scores for -partisan and -biparti 2e−05 2e−04 2e−03 0.2 0.3 0.4 Combined Threshold δ partisan bipartisan (b) 2e−05 2e−04 2e−03 0.2 0.3 0.4 Guncontrol Threshold δ partisan bipartisan (c) 1e−05 1e−04 1e−03 0.2 0.3 0.4 Obamacare Threshold δ partisan bipartisan (d) 

Research Question Are echo chambers consistent across social media? 

Data Table 1. For each data set, we report: the starting date of collec- tion T0, time span T expressed in days (d) or years (y), number of unique contents C, number of users N and coverage nc (fraction of users with classified leaning). For Twitter, T represents the window to sample active users, of which we retrieve all the tweets related to the topic via the API (more info in SI). Media Data set T0 T C N nc Twitter Gun control 06/2016 14 d 19 M 3963 0.93 Obamacare 06/2016 7 d 39 M 8703 0.90 Abortion 06/2016 7 d 34 M 7401 0.95 Facebook Sci/Cons 01/2010 5 y 75 172 183 378 1.00 Vaccines 01/2010 7 y 94 776 221 758 1.00 News 01/2010 6 y 15 540 38 663 1.00 Reddit Politics 01/2017 1 y 353 864 240 455 0.15 The Donald 01/2017 1 y 1.234 M 138 617 0.16 News 01/2017 1 y 723 235 179 549 0.20 Gab Gab 11/2017 1 y 13 M 165 162 0.13 what-is-pushshift-io/) at this link https://files.pushshift.io/gab/. Red- 401 11. AL Schmidt, et a 3035–3039 (2017 12. M Cinelli, et al., T 13. E Bakshy, S Mes facebook. Scienc 14. KH Jamieson, JN establishment. (O 15. RK Garrett, Echo news users. J. C 16. K Garimella, G D media: Echo cha 2018 World Wide Steering Commit 17. K Garimella, G D Attention on Con Web Science Con 18. W Cota, SC Ferr information sprea 19. JT Klapper, The e 20. RS Nickerson, C psychology 2, 17 21. M Del Vicario, et book. Sci. reports 22. A Bessi, et al., Sc one 10, e011809 23. CR Sunstein, The 

Methodology Independent ingredients Leaning (stance on a topic) Network (interaction substrate) Measures Structure (homophily in interactions) Bias (information diffusion) AAACF3icbZDLSsNAFIYnXmu9RV26GSyCq5CIohuh6MZlBXuBJobJdNJOO7k4MymWkLdw46u4caGIW935Nk7SLLT1h4GP/5zDmfN7MaNCmua3trC4tLyyWlmrrm9sbm3rO7stESUckyaOWMQ7HhKE0ZA0JZWMdGJOUOAx0vZGV3m9PSZc0Ci8lZOYOAHqh9SnGElluboB4YNLoU3uEzqGts8RTm2RBG46vLCyuxS5NIPYHWYFVV29ZhpmITgPVgk1UKrh6l92L8JJQEKJGRKia5mxdFLEJcWMZFU7ESRGeIT6pKswRAERTlrclcFD5fSgH3H1QgkL9/dEigIhJoGnOgMkB2K2lpv/1bqJ9M+dlIZxIkmIp4v8hEEZwTwk2KOcYMkmChDmVP0V4gFS2UgVZR6CNXvyPLSODevUMG9OavXLMo4K2AcH4AhY4AzUwTVogCbA4BE8g1fwpj1pL9q79jFtXdDKmT3wR9rnD39En4c= xi ⌘ Pai j=1 cj ai Follow 
 Co-comment 
 Reply 

Media-Bias Fact Check 0 100 200 300 400 500 Extreme Left Left Left−Center Least Biased Right−Center Right Extreme Right 

(a) Twitter (b) Reddit (c) Facebook (d) Gab Network Polarization and homophily in the local neighborhood 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 xN i ⌘ 1 k! i X j Aijxj 

(a) Twitter (b) Reddit (c) Facebook (d) Gab 1 10 100 1000 1 2 3 4 5 Community ID Community Size Against Abortion Pro Abortion 1 10 100 1000 10000 0 5 10 15 20 Community ID Community Size Extreme Left Extreme Right 101 103 105 0 20 40 60 Community ID Community Size Pro Vaccines Anti Vaccines 1 10 100 1000 10000 0 5 10 15 20 Community ID Community Size Extreme Left Extreme Right Communities Polarization and homophily in the community structure 

(a) Twitter (b) Reddit (c) Facebook (d) Gab � � � � � � � � � � � � � � � � � � � � � � −1.0 −0.5 0.0 0.5 1.0 −1.0 −0.5 0.0 0.5 1.0 Seed Leaning Influence Set Leaning 40 80 120 160 Influence Set Average Size � � � � � � � � � � � � � � � � � � � � � � � � −1.0 −0.5 0.0 0.5 1.0 −1.0 −0.5 0.0 0.5 1.0 Seed Leaning Influence Set Leaning 2000 2500 3000 3500 4000 Influence Set Average Size � � � � � � � � � � −1.0 −0.5 0.0 0.5 1.0 −1.0 −0.5 0.0 0.5 1.0 Seed Leaning Influence Set Leaning 1000 2000 3000 4000 Influence Set Average Size � � � � � � � � � � � � � � � � � � � � � � −1.0 −0.5 0.0 0.5 1.0 −1.0 −0.5 0.0 0.5 1.0 Seed Leaning Influence Set Leaning 100 200 300 Influence Set Average Size Dynamics Effects of information spreading (SIR) AAACMHicbVDLSgMxFM3UV62vqks3wSK4scyIokvRhbqrYFXo1CGTppo2yYx5iCWdT3Ljp+hGQRG3foXpY6GtBwKHc84l9544ZVRp33/zchOTU9Mz+dnC3PzC4lJxeeVCJUZiUsUJS+RVjBRhVJCqppqRq1QSxGNGLuP2Uc+/vCdS0USc605K6hzdCNqkGGknRcVjCENuIkuzkNwZeg+7IUf6FiNmT7OIdq/tVpC5jDI8si0YUgH/BDJo4UPUyqJiyS/7fcBxEgxJCQxRiYrPYSPBhhOhMUNK1QI/1XWLpKaYkawQGkVShNvohtQcFYgTVbf9gzO44ZQGbCbSPaFhX/09YRFXqsNjl+wtq0a9nvifVzO6uV+3VKRGE4EHHzUNgzqBvfZgg0qCNes4grCkbleIb5FEWLuOC66EYPTkcXKxXQ52y/7ZTungcFhHHqyBdbAJArAHDsAJqIAqwOARvIB38OE9ea/ep/c1iOa84cwq+APv+wfsHKoh µi ⌘ |Ii | 1 X j2Ii xj 

1 10 100 1000 10000 2 4 6 8 10 12 Community ID Community Size Extreme Left Extreme Right 1 10 100 1000 0 10 20 30 40 Community ID Community Size Extreme Left Extreme Right   eaning   eaning 600 700 800 900 Influence Set Average Size 1 10 100 1000 10000 2 4 6 8 10 12 Community ID Community Size Extreme Left Extreme Right 1 10 100 1000 0 10 20 30 40 Community ID Community Size Extreme Left Extreme Right ï ï    ï ï    Seed Leaning Influence Set Leaning  10  20 Influence Set Average Size ï ï    ï ï    Seed Leaning Influence Set Leaning 600 700 800 900 Influence Set Average Size (a) Facebook (b) Reddit 2 4 6 8 10 12 Community ID ï ï    ï ï    Seed Leaning Influence Set Leaning  10  20 Influence Set Average Size ï ï    Influence Set Leaning (a) Facebook Extreme Right 1 10 100 1000 10000 2 4 6 8 10 12 Community ID Community Size Extreme Left Extreme Right 1 10 100 1000 0 10 20 30 40 Community ID Community Size Extreme Left Extreme Right   Influence Set 1 10 100 1000 10000 2 4 6 8 10 12 Community ID Community Size Extreme Left Extreme Right 1 10 100 1000 0 10 20 30 40 Community ID Community Size Extreme Left Extreme Right ï ï    ï ï    Seed Leaning Influence Set Leaning  10  20 Influence Set Average Size ï ï    ï ï    Seed Leaning Influence Set Leaning 600 700 800 900 Influence Set Average Size (a) Facebook (b) Reddit Reddit 
 News Facebook 
 News 

Is there an echo chamber on political Reddit? Research Question 

Data 2016 US Presidential Elections r/politics as a "neutral" ground r/The_Donald and r/hillaryclinton, r/HillaryForAmerica as home communities Table 1. Main properties of the Politics network: number of users N, divided in Trump/Clinton supporters NT / NC, number of links E, average degree hki, reciprocity r (fraction of bidirectional links over the total), and total number of interactions W. N NT NC E hki r W 31218 27012 4206 500030 16.02 0.4482 716765 other users visiting the same subreddit. Upvotes are generally understood to encode approval, appreciation, or agreement; 

Data Model Each node has a label in {T,C} (depending on their home community) P(T) ≃ 0.87 for Trump, P(C) ≃ 0.13 for Clinton Directed network of replies, weight = # of replies Activity = out-weight of a node Users can upvote posts/comments 

These characteristics can be further inspected by con X node to a Y node, given that the first node has leaning P(X ! Y|X) = P(X ! Y) P(X !) = WXY WX! ' 0 @ Author T C By looking at the columns of Eq. (2), in absence of h column to be equal: given the author of a comment, th only by the size of the group. Instead, we can observe t (72% of interactions) than Trump supporters themselves supporters, who are more likely to interact with Clinton (28% of interactions). These intuitions will be solidified social interactions. Finally, we compare the average sentiment polarity polarity (ranging from 1 to 1) of the textual content o Link Conditional Probability Absence of homophilic or heterophilic effects would imply each column to be equal Instead, C interacts more with T and vice-versa (heterophily) Is there a clear pattern? These characteristics can be further inspected by considering the conditional probab X node to a Y node, given that the first node has leaning X, P(X ! Y|X) = P(X ! Y) P(X !) = WXY WX! ' Target T C 0 @ 1 A Author T 0.62 0.38 C 0.72 0.28 . By looking at the columns of Eq. (2), in absence of homophilic or heterophilic effec 

Null Model No homophily or heterophily Takes into account label priors Preserves degree sequences (con fi guration model) Equivalent to reshuf fl ing links while preserving in/out-strength The RN model preserves both the in- and following the so called configuration model node to a Y node, given that the first node ha pRN(X ! Y|X) = W!Y W ' Author T C In the following, we investigate deviation Deviation of conditional and joint pro The difference between the empirical and ra Figure 2 (a). Cross-interactions between opp a RN model, with an odds ratio of 1.195. Th pRN(X ! Y) = WX!W!Y W2 ' Target T C 0 @ 1 A Author T 0.43 0.225 C 0.225 0.12 . The RN model preserves both the in- and out-strength sequence of node following the so called configuration model [37]. In this RN model, the co node to a Y node, given that the first node has leaning X, reads pRN(X ! Y|X) = W!Y W ' Target T C 0 @ 1 A Author T 0.66 0.34 C 0.66 0.34 . In the following, we investigate deviations of observed data from this RN These characteristics can be further inspected by considering the conditional proba X node to a Y node, given that the first node has leaning X, Target T C 0 1 r 

Deviation from Null Model Heterophily Positive off-diagonals Asymmetry Different off-diagonals Conditional 

Logit Regression Model Model probability u→v from binary features (represent all 4 possible cases) Label(u) Label(u) ≠ Label(v) Interaction between these two Confounders: score, difference in score Activity taken into account by null model via negative sampling strategy 
 (choose u proportional to out-strength, v proportional to in-strength) 

ratios obtained by logistic regression. Each column corresponds to a model with a specific set of variables: we features in the first column; then, we add to the model the first, the second, and both sets of confounding e variables shown here have a statistically significant (p < 0.001) impact on the likelihood of writing a Variable name Comm. Conf. 1 Conf. 2 Conf. 1+2 Clinton sup. 0.942*** 0.918*** 0.936*** 0.911*** Cross-group 1.195*** 1.172*** 1.191*** 1.165*** Clinton sup., Cross-group 1.064*** 1.091*** 1.070*** 1.102*** Avg. score (author) 1.166*** 1.174*** Avg. score (target) 1.151*** 1.167*** Diff. avg. score 1.213*** 1.228*** Diff. frac. positive 0.497*** 0.498*** Frac. positive (author) 1.260*** 1.247*** Frac. positive (target) 1.221*** 1.195*** * p < 0.05, *** p < 0.001 exists, we discard it. This way, the negative sample reflects exactly the null model presented in Section 3: the onsidering a pair of nodes is just the product of two independent probabilities – the probability that a node u action, and the probability that a node v receives it. The role of logistic regression is thus to capture how the sider alter the chances of observing a link u ! v. Odds ratios & Interaction Matrix 

ratios obtained by logistic regression. Each column corresponds to a model with a specific set of variables: we features in the first column; then, we add to the model the first, the second, and both sets of confounding e variables shown here have a statistically significant (p < 0.001) impact on the likelihood of writing a Variable name Comm. Conf. 1 Conf. 2 Conf. 1+2 Clinton sup. 0.942*** 0.918*** 0.936*** 0.911*** Cross-group 1.195*** 1.172*** 1.191*** 1.165*** Clinton sup., Cross-group 1.064*** 1.091*** 1.070*** 1.102*** Avg. score (author) 1.166*** 1.174*** Avg. score (target) 1.151*** 1.167*** Diff. avg. score 1.213*** 1.228*** Diff. frac. positive 0.497*** 0.498*** Frac. positive (author) 1.260*** 1.247*** Frac. positive (target) 1.221*** 1.195*** * p < 0.05, *** p < 0.001 exists, we discard it. This way, the negative sample reflects exactly the null model presented in Section 3: the onsidering a pair of nodes is just the product of two independent probabilities – the probability that a node u action, and the probability that a node v receives it. The role of logistic regression is thus to capture how the sider alter the chances of observing a link u ! v. Odds ratios & Interaction Matrix 

ratios obtained by logistic regression. Each column corresponds to a model with a specific set of variables: we features in the first column; then, we add to the model the first, the second, and both sets of confounding e variables shown here have a statistically significant (p < 0.001) impact on the likelihood of writing a Variable name Comm. Conf. 1 Conf. 2 Conf. 1+2 Clinton sup. 0.942*** 0.918*** 0.936*** 0.911*** Cross-group 1.195*** 1.172*** 1.191*** 1.165*** Clinton sup., Cross-group 1.064*** 1.091*** 1.070*** 1.102*** Avg. score (author) 1.166*** 1.174*** Avg. score (target) 1.151*** 1.167*** Diff. avg. score 1.213*** 1.228*** Diff. frac. positive 0.497*** 0.498*** Frac. positive (author) 1.260*** 1.247*** Frac. positive (target) 1.221*** 1.195*** * p < 0.05, *** p < 0.001 exists, we discard it. This way, the negative sample reflects exactly the null model presented in Section 3: the onsidering a pair of nodes is just the product of two independent probabilities – the probability that a node u action, and the probability that a node v receives it. The role of logistic regression is thus to capture how the sider alter the chances of observing a link u ! v. Odds ratios & Interaction Matrix (ii) Clinton supporters are less likely to l (iii) however, Clinton supporters are asymm to supports the other candidate (odds We can also compute the interaction mat model for each of the four possible combin Target T C 0 @ 1 A Author T 0.925 1.105 C 1.107 0.871 The results obtained via this methodology a Then, we control for the other Reddit v can be explained by considering these other 

(28% of interactions). These intuitions will social interactions. Finally, we compare the average sentim polarity (ranging from 1 to 1) of the textu average values according to the possible pair Target T C 0 @ 1 A Author T 1.26 0.72 C 1.10 5.75 ⇥10 2. First, we observe that interactions within T (average sentiment of 0.0575 vs 0.0126). I Sentiment T more negative sentiment than C Sentiment more negative in cross-interactions 

Research Question Are there sociodemographic factors? 

Hyp. 1: Ideological Echo Chambers 
 Ideological sides only talk among themselves 

Hyp. 1: Ideological Echo Chambers 
 Ideological sides only talk among themselves 

Hyp. 2: Demographic Factors 
 Demographic groups and classes grow apart, and reinforce ideological identity 

Hyp. 2: Demographic Factors 
 Demographic groups and classes grow apart, and reinforce ideological identity 

Data News Discussion on Reddit Interactions among users 5 years, 2016-2021 One network per year 21k to 34k users, ~1M interactions Four axes: Age, Gender, Af fl uence, Politics 
 [Waller & Anderson, Nature 2021] 

Groups of node u Probability of u interacting with v Groups of node v Regression Model 

Regression Model Log odds ratio given by 
 a pair of features 

No content

No content

No content

No content

Is this only a result of 
 different news topics? 

For each interaction, we identify the topic of the news related to that interaction 

We add it to the regression model 

We add it to the regression model 

No content

Research Question Is a single ideological axis too simple? 

Authoritarian Libertarian Left Right Authoritarian Right Authoritarian Left Libertarian Right Libertarian Left economic axis social axis Jan Cli ff ord Lester. 1996. The poli ti cal compass and why libertarianism is not right-wing. Journal of Social Philosophy 27, 2 Political Compass 

How do Political and Demographic Groups interact? Con fl ict? Af fi nity? 

80k posts 1M comments 400k posts 22M comments 2020 - 2022 user A user B Data 

Authoritarian Libertarian Left Right Authoritarian Right Authoritarian Left Libertarian Right Libertarian Left economic axis social axis Data 

Interactions Between Political Opinions Target Opinion Y Source Opinion X A B User A comments on User B 

Homophily & Heterophily 

Homophily in the Social Axis 

Heterophily in the Economic Axis 

Empty cells correspond to non-statistically signi fi cant results ( ) α = 0.05 Homophily in Demographics 

Empty cells: non statistically signi fi cant results ( ) α = 0.05 Homophily in Demographics 

Language Toxicity in Interactions https://perspectiveapi.com τ : X → [0,1] 

Heterophilic interactions are toxic 

Alternative Viewpoints Are we sure about the role of echo chambers? 

Echo chambers are de fi ned by con fl ict, not isolation Social media fosters non-local interactions that may drive affective polarization Not by isolating us in echo chambers that shield us from other viewpoints But by connecting us to views and positions outside our local bubble Social media as spaces for social identity formation (not opinion formation) No interactions with random nodes All interactions with random nodes Petter Törnberg, “How digital media drive affective polarization through partisan sorting”, PNAS 2022 

Echo chambers are de fi ned by con fl ict, not isolation Social media fosters non-local interactions that may drive affective polarization Not by isolating us in echo chambers that shield us from other viewpoints But by connecting us to views and positions outside our local bubble Social media as spaces for social identity formation (not opinion formation) No interactions with random nodes All interactions with random nodes Petter Törnberg, “How digital media drive affective polarization through partisan sorting”, PNAS 2022 Back fi re E ff ect 

Facebook Echo Chambers Study Intervention: algorithmically reduced exposure to content from like-minded sources by about one-third No signi fi cant impact on: 
 affective polarization, ideological extremity, candidate evaluations, 
 belief in false claims B. Nyhan et al. “Like-minded sources on Facebook are prevalent but not polarizing”, Nature 2023 

The Marketplace of Rationalizations Echo chambers are not a cause of polarization They are an effect driven by posthoc rationalization “Demand side” explanation: 
 social structures in which agents compete 
 to produce rationalizations for money and social rewards If we were not buying it, they would not sell it 

Summary Operational de fi nition of echo chambers across social media Echo chambers on generalist social networks (Twitter and Facebook), 
 but not on topical social fora (Reddit and Gab) Selection bias might be an explanation for the differences Ideologic heterophily on Reddit, but driven by con fl ict along the economic (left-right) axis Ideologic af fi nity on the social (lib-auth) axis and demographic homophily Are echo chambers a consequence rather than a cause of polarization? 

K. Garimella, G. De Francisci Morales, A. Gionis, M. Mathioudakis 
 “Political Discourse on Social Media: Echo Chambers, Gatekeepers, and the Price of Bipartisanship” 
 WebConf 2018 M, Cinelli, G. De Francisci Morales, A. Galeazzi, W. Quattrociocchi, M. Starnini 
 “The Echo Chamber Effect on Social Media” 
 PNAS 2021 G. De Francisci Morales, C. Monti, M. Starnini 
 “No Echo in the Chambers of Political Interaction on Reddit” 
 SciRep 2021 C. Monti, J. D’Ignazi, M. Starnini, G. De Francisci Morales 
 “Evidence of Demographic rather than Ideological Segregation in News Discussion on Reddit” 
 WebConf 2023 E. Colacrai, F. Cinus, G. De Francisci Morales, M. Starnini 
 “Navigating Multidimensional Ideologies with Reddit’s Political Compass: Economic Con fl ict and Social Af fi nity” 
 WebConf 2024 64 [email protected] https://gdfm.me @gdfm7 

Appendix 

Reddit Politics Activity vs Leaning 1 10 100 1000 10000 −1.0 −0.5 0.0 0.5 1.0 Individual Leaning Activity