Accept, Sample) "The Nature and Origins of Mass Opinion" Response Axiom: "Individuals form opinions by averaging across the considerations that are immediately salient or accessible to them" Authoritative (influential) users with high degree set opinions Measure likelihood of user to be exposed to opinions from influential users on either side
walk that starts from a random vertex in tha visits any high-degree vertex (from either sid dom Walk Controversy (RWC) measure as fo ending in partition X and one ending in par obabilities of two events: (i) both random wa in and (ii) both random walks started in a pa The measure is quantified as RWC = PXX PY Y PY X PXY , X, Y } is the conditional probability AB = Pr[start in partition A | end in partition probabilities have the following desirable prop Consider two random walks, one ending in partition X and one ending in partition Y , RWC is the difference of the probabilities of two events: (i) both random walks started from the partition they ended in and (ii) both random walks started in a partition other than the one they ended in (a) (b) Partitions obtained for (a) #beefban, (b) #russia march by using the hybrid graph ch. The partitions are more noisy than those in Figures 3(a,b). Subsequently, we select one partition at random (each with probability 0 er a random walk that starts from a random vertex in that partition. Th nates when it visits any high-degree vertex (from either side). define the Random Walk Controversy (RWC) measure as follows. “Consi m walks, one ending in partition X and one ending in partition Y , RWC nce of the probabilities of two events: (i) both random walks started fr on they ended in and (ii) both random walks started in a partition other t ey ended in.” The measure is quantified as RWC = PXX PY Y PY X PXY , PAB , A, B 2 {X, Y } is the conditional probability PAB = Pr[start in partition A | end in partition B]. orementioned probabilities have the following desirable properties: (i) they d by the size of each partition, as the random walk starts with equal pro ach partition, and (ii) they are not skewed by the total degree of vertices
Random walks end on either side with equal probability Not skewed by size of each partition Not skewed by total degree of vertices in each partition Close to 1 when probability of crossing sides low (high controversy) Close to 0 when probability of crossing comparable to that of staying (low controversy)
os-R´ enyi graphs planted with two communities. p1 is the intra-community edge probability, while p2 is the inter-community edge probability. generate random Erd¨ os-R´ enyi graphs with varying community structure, and compute the RWC score on them. Specifically, to mimic community structure, we plant two separate communities with intra-community edge probability p1 . That is, p1 defines how dense these communities are within themselves. We then add random edges between these two communities with probability p2 . Therefore, p2 defines how connected the two communities are. A higher value of p1 and a lower value of p2 create a clearer two-community structure. Figure 10 shows the RWC score for random graphs of 2000 vertices for two different settings: plotting the score as a function of p1 while fixing p2 (Figure 10a), and vice-versa Planted Synthetic Graphs
a topic is on social media Graph-based measure: no domain knowledge, language agnostic Intuitive semantics founded on opinion formation models Captures controversy better than state-of-the-art User-level polarization measure easy to derive
the activity in the retweet network. An increase in interest in the controversial topic corresponds to an increase in the controversy score of the retweet network. 5.1 Network F t r s w
activity in the retweet network. As the interest increases, the num- ber of core-periphery edges, normalized by the expected number of edges in a random network, increases. This sug- gests a propensity of periphery nodes to connect with the core nodes when interest increases.
of echo chambers ("Hear your own voice") Might hamper deliberative process in democracy Lack of shared world view Concern expressed by former US Presidents, Facebook, Twitter, and more
content + network definition Echo chamber = political leaning of content that users receive from network agrees with that of content they share to the network
domains) Score derived by self-declared affiliation of sharers on FB FoxNews.com is aligned with conservatives (CP = 0.9), HuffingtonPost.com is aligned with liberals (CP = 0.17)
Production score Average political leaning of the content the user tweets Consumption score Average political leaning of the content the user receives on their feed Results of selection by the user
e e k Figure 1: Example showing the denition 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.
content with polarity within δ δ-consumer: consumes content with polarity beyond δ δ-gatekeeper: δ-partisan but not δ-consumer consumes from both sides but produces content aligned with only one side blocks information flow towards its community
Figure 3: Distribution of production and consumption polarity, for P (rst row) and NP (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 (a) (b) (c) (d) (e) (f) (g) (h) (i) (j) Figure 3: Distribution of production and consumption polarity, for P (rst row) and NP (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.
and consumption polarity, for P (rst row) and NP (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. (a) (b) (c) (d) (e) (f) (g) (h) (i) (j) Figure 4: Top: Production polarity variance vs. production polarity (mean). Bottom: Consumption polarity variance vs. con- sumption polarity (mean). However, dierently from the rest of the side they align with, they show a lower clustering coecient, an indication that they are not completely embedded in a single community. Given that they receive content also from the opposing side, this result is to be Finally, given that both partisans and gatekeepers sport higher centrality, we compare their PageRank values directly and nd that there is a signicant dierence: partisans have a higher PageRank compared to gatekeepers (gure not shown). This eect is more Variance (f) (g) (h) (i) (j) Figure 3: Distribution of production and consumption polarity, for P (rst row) and NP (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. (a) (b) (c) (d) (e) (f) (g) (h) (i) (j) Figure 4: Top: Production polarity variance vs. production polarity (mean). Bottom: Consumption polarity variance vs. con- sumption polarity (mean). However, dierently from the rest of the side they align with, they show a lower clustering coecient, an indication that they are not completely embedded in a single community. Given that they receive content also from the opposing side, this result is to be Finally, given that both partisans and gatekeepers sport higher centrality, we compare their PageRank values directly and nd that there is a signicant dierence: partisans have a higher PageRank compared to gatekeepers (gure not shown). This eect is more
bipartisan (a) 0.0 1.0 2.0 0.2 0.3 0.4 Combined Threshold δ partisan bipartisan (b) −0.5 0.5 1.5 2.5 0.2 0.3 0.4 Guncontrol Threshold δ partisan bipartisan (c) 0.0 1.0 2.0 0.2 0.3 0.4 Obamacare Threshold δ partisan bipartisan (d) 0.0 1.0 2.0 0.2 0.3 0.4 Abortion 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 signicantly higher for gatekeepers < 0.001) for at least 4 of the 6 thresholds used. A mi- s next to the checkmark (-) indicates that the property is nicantly lower. 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 The last two columns show results for all features combin p (net) (net) p (n-gram) (n-gram) p Price of Bipartisanship 0.0 1.0 2.0 0.2 0.3 0.4 Large Threshold δ partisan bipartisan (a) 0.0 1.0 2.0 0.2 0.3 0.4 Combined Threshold δ partisan bipartisan (b) −0.5 0.5 1.5 2.5 0.2 0.3 0.4 Guncontrol Threshold δ partisan bipartisan (c) 0.0 1.0 2.0 0.2 0.3 0.4 Obamacare Threshold δ partisan bipartisan (d) 0.0 1.0 2.0 0.2 0.3 0.4 Abortion 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 signicantly higher for gatekeepers < 0.001) for at least 4 of the 6 thresholds used. A mi- s next to the checkmark (-) indicates that the property is nicantly lower. 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 The last two columns show results for all features combin p (net) (net) p (n-gram) (n-gram) p
of pro- urce pro- the and ddi- for ties. (for and mp- also pro- rces. ach The Table 2: Comparison of various features for partisans & bi- partisans and gatekeepers & non-gatekeepers. A 3 indicates that the corresponding feature is signicantly higher for the group of the column (p < 0.001) for at least 4 of the 6 thresh- olds used, for most datasets. A minus next to the check- mark (-) indicates that the feature is signicantly lower. Features Partisans Gatekeepers PageRank 3 3 clustering coecient 3 (-) 3 (-) user polarity 3 (-) 3 (-) degree 3 3 retweet rate 3 7 retweet volume 3 7 favorite rate 3 7 favorite volume 3 7 # followers 7 7 # friends 7 7 # tweets 7 7 age on Twitter 7 7 datasets).9 A “3 (-)” means that the property is signicantly lower
of echo chambers with two elements: Content (echo) + Network (chamber) Data supports the selective exposure theory Bi-partisan users pay a price in terms of network centrality and content appreciation
the first step (RWC) Controversies are dynamic (time is an important factor) Collective attention increases polarization Echo chambers associated with controversies Evidence of selective exposure and price of bi-partisanship
data to opinion dynamics models Temporal dynamics of the process Application to other contexts (Reddit, Facebook) Interventions: can we do something about it?