Reconceptualizing Cross-Cutting Political Expression on Social Media: A Case Study of Facebook Comments During the 2016 Brexit Referendum

ABSTRACT Political communication research has long sought to understand the effects of cross-cutting exposure on political participation. Here, we argue for a paradigm shift that acknowledges the agency of citizens as producers of cross-cutting expression on social media. We define cross-cutting expression as political communication through speech or behavior within a counter-attitudinal space. After explicating our conceptualization of cross-cutting expression, we empirically explore: its extent, its relationship to political arguments, and its implications for digital campaigning during the 2016 Brexit Referendum. Our dataset, comprising 2,198,741 comments from 344,884 users, is built from Facebook comments to three public campaign pages active during the Brexit referendum: StrongerIn, VoteLeave, and LeaveEU. We utilize reactions data to sort partisans into “Remain” and “Brexit” camps and, thereafter, chart users’ commenting flows across the three pages. We estimate 29% of comments to be cross-cutting, and we find strong correlations between cross-cutting expression and reasoned political arguments. Then, to better understand how cross-cutting expression may influence political participation on social media, we topic model the dataset to identify the political themes discussed during the Brexit debate on Facebook. Our findings suggest that political Facebook pages are not echo chambers, that cross-cutting expression correlates with reasoned political arguments, and that cross-cutting expression may influence the online voter mobilization potential of political Facebook pages.


Introduction
Cross-cutting exposure typically refers to coming into contact with political viewpoints different than one's own beliefs.Sparked by earlier findings that exposure to cross-cutting views depresses electoral participation (Mutz, 2002), political communication scholars have sought to investigate how cross-cutting exposure affects political behavior.A recent synthesis of this literature finds no consistent correlation between cross-cutting exposure and online or offline political participation (Matthes et al., 2019).However, in following the broader "reception-effects paradigm" in communication research (Shah, 2016, p. 13), these studies tend to overemphasize information exposure at the expense of civic agency.
Democratic citizens are not merely passive receivers of information; they are also active producers of communication in private, public, and digitally-mediated spaces.Therefore in this study, we take a different approach to cross-cutting that highlights the political agency of citizens on social media.Instead of examining the effects of cross-cutting exposure on political participation, we consider cross-cutting expression as a form of political participation.We define cross-cutting expression as political communication through speech or behavior within a counter-attitudinal space.After explicating our theoretical understanding of cross-cutting expression, we adopt an exploratory research design that investigates crosscutting expression in the comment fields of political Facebook pages.Leveraging the collapsed political terrain of the 2016 Brexit Referendum, we quantify the extent of crosscutting expression in Facebook comments, examine its relationship to political argumentation, and interpret the implications of cross-cutting expression for digital campaigning and online voter mobilization.

From Cross-Cutting Exposure to Cross-Cutting Expression
Our understanding of cross-cutting expression does not simply reverse the direction of communication implied by cross-cutting exposure -i.e., that a citizen shifts from a passive receiver to active sender of cross-cutting views.Instead, we argue for a conceptual decoupling of "cross-cutting" and "expression," and the core theoretical arguments of our study are three-fold.First, cross-cutting should be defined by the context -not content -of online conversations.Second, political expression should not be constrained to the explicit verbalization of political opinions.And third, the ways that both cross-cutting and expression manifest on social media will be shaped by a platform's digital architecture.We explicate each argument in turn.

Cross-Cutting is More Than Content
Traditionally, cross-cutting is defined by the content of discourse and is often conceptualized narrowly as disagreement.For example, scholars have defined cross-cutting exposure as the "disagreement in viewpoints encountered by individuals" (Matthes et al., 2019) and cross-cutting discussions as "disagreement and opposing viewpoints when discussing political and public affairs" (Chan et al., 2021, p. 2).While these definitions are not incorrect, we identify two risks that arise from such a narrow construal of cross-cutting when applied to social media.
First, since disagreement correlates with incivility in Facebook comments (Rossini, 2022), placing a primacy on disagreement may bias the concept of cross-cutting toward normatively negative forms of discursive interaction on social media.Second, constraining cross-cutting to disagreement risks omitting other meaningful forms of social media interactions around elections, parties, and policies.For example, if a staunch liberal and conservative express bipartisan agreement about a policy on social media (e.g., ending an unpopular war), is this not a normatively positive form of cross-cutting interaction?
We argue that it is, because we define cross-cutting by the context of online interactions, rather than their content.As a concept developed prior to social media, "cross-cutting" was originally operationalized through offline network structures (Mutz, 2002), which are contextual for each individual.Similarly, the ideological configuration of one's online network constitutes a contextual network property.Therefore, we argue that online interactions between ideologically opposed individuals should be considered cross-cutting at the network level, even if the content of their interactions is not explicitly about exchanging political viewpoints.This understanding aligns more closely with Goldman and Mutz (2011, p. 48), who later defined cross-cutting as "when the perceived political leaning of the source is distant from the political leaning reported by the respondent."Here, crosscutting is conceptualized as the ideological distance between a media source and consumer, rather than the content of the media itself.
We extend the same contextual dynamic to ideological differences between political partisans and their interactions within online spaces.Especially since digital forms of user expression and interaction can vary by platform, our definition of cross-cutting emphasizes the counter-attitudinal aspect at the space of interaction (rather than the form or content of expressions as such).We therefore consider cross-cutting to comprise all interactions between opposing partisans, as well as between partisan users and online spaces developed to promote an opposing political agenda.This leads to our second core argument: that political expression on social media is broader than verbalized opinions.

Political Expression is Broader Than Opinions
The literature on cross-cutting exposure overly emphasizes citizens as passive receivers of information.During electoral contests, citizens can actively inform and mobilize peers on social media (Dutceac Segesten & Bossetta, 2017).Moreover, they can seek out users holding counter-attitudinal viewpoints, attempt to persuade them, or even troll them.For the individual citizen, such online expressions shape self-identification with the democratic process (Lane et al., 2019) and actualize discursive participation in digital realms (Shah, 2016).Certainly, not all online political expressions are well-formulated opinions that exemplify deliberative ideals (Freelon, 2015).In fact, political expressions comprise a wider array of discourses than verbalized opinions altogether.Penney (2017) charts the historical lineage of political expression via material objects such as yard signs and clothing, and he draws parallels to non-verbal, digital manifestations such as changing one's profile picture to support a political cause.
Thus, political expression is not only about words; it is also about actions.Patterns of action can be socially meaningful (Adler & Pouliot, 2011, p. 6), and research finds that lifestyle choices, such as one's choice of entertainment or leisure activities, can correlate with political ideology (DellaPosta et al., 2015).Other behaviors spanning consumer boycotts, vandalism, and even violence can effectively convey a political opinion without words.Here again, context plays a crucial role.Wearing a white suit to a dinner party is apolitical, but female lawmakers wearing white suits in unison can send a powerful message about women's rights.Following this line of argument, we contend that on social media, digital presence can constitute a meaningful form of political expression.
Protesters, activists, and even insurrectionists can express political opinions through physical presence.On social media, displays of digital presence such as Zoom-bombing, Twitch-raiding, or Twitter hashtag-hijacking can similarly be considered acts of political expression.Each seeks to disrupt established communication flows and may or may not be accompanied by verbalized opinion statements.In our view, the lack of verbalizing opinions does not preclude acts of presence from being politically meaningful or consequential.If users demonstrate their digital presence in a counter-attitudinal space, and these demonstrations relate in some way to politics, we consider these online actions as forms of crosscutting expression.
Surely, the verbal expression of political opinions to users holding opposing views constitutes one form of cross-cutting expression.However, stating an opinion is not the only method of political expression available in the modern political action repertoire.Thus, our theoretical thrust is to highlight the important role of context in operationalizing cross-cutting and in particular, how demonstrations of presence play a key role in crosscutting expression for certain digital environments.On Facebook, a user's navigating to and interacting with a counter-attitudinal page would constitute cross-cutting expression, even if that user does not articulate an explicit political opinion through words or text.This brings us to our third core argument: that a platform's digital architecture will shape how both cross-cutting and political expression manifest in online spaces.

Facebook Pages as Dual Constructs
On social media, the opportunity for cross-cutting expression depends on how digital spaces are designed, as well as how partisanship can be conveyed to users technically (via platform features) and socially (via communication norms).While platform structures do not technologically determine what users say or do on social media, the computational rule systems that comprise these structures mediate how speech and behavior are digitally rendered.Thus, we argue that a platform's architecture gives form to -or shapes -the opportunity structures for political expression in terms of the digital manifestations it can take and to whom it can reach online.
Facebook's digital architecture, for example, allows political actors to establish public pages to promote their ideological positions (Bossetta, 2018).Posts issued by these pages open up spaces that can host cross-cutting expressions (e.g., Facebook comments and reactions).Rather than conceptualize these features as affordances, we approach them as the architectural facts of how Facebook was designed in 2016.This architectural approach forces us to consider how the structural context of the digital environment we study relates to our behavioral phenomenon of interest.By doing so, we argue that Facebook pages have remained undertheorized and operate both as static and dynamic constructs, each with ramifications for cross-cutting expression.
In the static understanding, Facebook pages function similarly to websites by providing users with a stable digital space to learn more about the page owner, obtain contact information, and peruse posts in reverse chronological order.Although user engagement with political pages is concentrated among relatively few users (Nielsen & Vaccari, 2013), the static quality of pages opens up a space for politically interested, like-minded users to congregate.Yet, a key design choice by Facebook is that public pages are open for anyone to view, react, or comment.This sets pages apart from Facebook groups, which can set up stricter moderation protocols that work as gatekeeping mechanisms.The relative absence of gatekeeping in public pages limits their ability to seal off opposing opinions.Therefore, political Facebook pages can function both as a "home base" for the like-minded and a "sitting target" for users holding opposing views.
At the same time, Facebook pages are also dynamic constructs, since posts issued by a page are individually and ephemerally inserted into a user's Feed.These posts can cascade across user networks through organic interactions such as sharing, or users can be exposed to posts through paid targeting by page managers or algorithmic filtering by the platform.For example, prior research demonstrates that Facebook's algorithms can expose users to counter-attitudinal information from public pages (Bakshy et al., 2015).This creates the opportunity for incidental exposure that has been found to motivate cross-cutting discussions on social media (Kwak et al., 2020).Thus, the opportunity structures for cross-cutting expression are available when users intentionally visit a page (in the static sense) or when they are incidentally exposed to a page's posts in their Feed (in the dynamic sense).These opportunity structures, and users' ability to leverage them, are shaped by Facebook's digital architecture.
Such platform contexts may further mediate users' likelihood to express political disagreement, which we have argued is an overly narrow operationalization of cross-cutting that is conceptually problematic.The reasons buttressing this argument are that equating cross-cutting with disagreement: risks neglecting the agency of citizens as producers of cross-cutting content, constrains political expression to explicit opinion formation, and fails to consider how digital architectures shape user interactions.To empirically illustrate why these oversights matter, we adopt an exploratory research design that investigates the quantity, content, and implications of cross-cutting expression on Facebook.

Exploratory Design and Research Questions
Exploratory research designs presume that findings are data-dependent, and this presumption is well suited for social media research generally and studies of Brexit in particular.Since platform architectures and audiences change over time, there is no guarantee that findings from previous studies will apply to future cases.Moreover, the case of Brexit offers a rare opportunity to collapse the British multi-party system into binary polls (i.e., "Remain In" or "Leave" the European Union).Thus, we purposefully select Brexit as a case study, since it offers a simplified political terrain to operationalize cross-cutting expression.However, given the unique context of Brexit in tandem with Facebook's architecture at one point in time, we opt for an exploratory research design without a priori hypothesis formulation.

Research Questions
Instead, we pose three open-ended research questions.The first is RQ1: To what extent does cross-cutting expression occur in Facebook comments?To date, research investigating crosscutting discussions on social media is primarily survey-based (Chan et al., 2021, Lu & Lee, 2020;Kwak et al., 2020).While helpful to explore the antecedents of cross-cutting expression, these surveys rely on self-perceptions of cross-cutting discussion frequency that likely do not align with real-world behavior.Moreover, by focusing conceptually on discussions, these studies tend to reproduce the existing norm of constraining expression to verbalized opinions and more specifically, disagreement.
Although no study has explicitly quantified cross-cutting expression on Facebook, prior research suggests that it does occur.In a qualitative study of Facebook pages during the 2011 Danish election, Schwartz (2015, p. 7) spots early examples of comments exhibiting "radical criticism from people who clearly belong on the opposite side of the political spectrum."Similarly, Valera-Ordaz (2019) finds in the 2015 Spanish elections that 11% of comments to national party pages expressed opinions counter to the party's ideology.These studies show that comments do not always align with a page's ideology, thus providing a motivation to further investigate the extent of cross-cutting expression.
Second, we ask RQ2: What is the relationship between cross-cutting expression and reasoned political arguments?Since cross-cutting is predominantly conceptualized as content (i.e., disagreeing opinions), we developed RQ2 to compare our context-based understanding of cross-cutting from RQ1 against more traditional, content-based measures.This comparison allows us to approximate how two different measures of cross-cutting -content-based versus context-based -may affect our aggregate reporting of cross-cutting expression derived from RQ1.We chose political arguments as our content measure, since arguments contain the types of justified opinions that correlate with disagreement in Facebook comments (Rossini, 2022).In addition to being a proxy for disagreement, reasoned arguments signify the type of thought formulation, message articulation, and response anticipation that "shape participatory engagement" (Shah, 2016, p. 13) in meaningful ways that existing frameworks of deliberation do not capture.Thus, our focus on arguments provides a strict, content measure for cross-cutting while also broadening the purview of online deliberation research with a substantive, rather than normative, measure of online discursive participation.
Third, we ask RQ3: What is the relationship between cross-cutting expression and political topics discussed during the Brexit referendum on Facebook?Whereas RQ2 investigates whether cross-cutting expression influences the rhetorical presentation of political discourse (i.e., arguments versus non-arguments), RQ3 explores whether the content of political topics differs based on whether they were issued to cross-cutting spaces or likeminded ones.Since we have argued that cross-cutting expression is a context-dependent concept related to user-network properties, RQ3 examines whether changes in the context of conversation (namely, the ideological configuration of a digital space) affects the content of conversation at the level of topics discussed.Further, the inclusion of this research question allows us to probe the overall relationships between cross-cutting expression as an activity (RQ1), reasoned political arguments as rhetorical delivery (RQ2), and the topical content of Facebook comments themselves (RQ3).

Methodology
To answer these research questions, we conduct a descriptive analysis of Facebook comments to three pages campaigning for the 2016 Brexit referendum.The study's dataset 1 includes posts, comments, and reactions from three political campaign pages 2 -StrongerIn, VoteLeave, and LeaveEU.Whereas StrongerIn and VoteLeave were the two official campaigns, LeaveEU remained a prominent grassroots player after failing to become the official Leave campaign.The timeframe of study is February 3rd -August 31st, 2016, which covers the 10-week official campaign (April 15th to June 23rd) as well as 10 weeks before and after the vote.This broad timeframe ensures that our findings are not overly influenced by key electoral events, such as the final result.The data was collected in 2017 using the VoxPopuli harvester (Bonacci et al., 2016), which calls Facebook's Graph API and stores the output in a secure SQL database maintained by Lund University.The dataset comprises 1,978 posts and 2,198,741 comments from 344,884 users.
Our methodology is divided into three parts to answer each research question, respectively.For RQ1, we provide a descriptive measurement of the quantity and directional flow of crosscutting comments.For RQ2, we manually annotate reasoned political arguments in a sample of 5,000 comments and test whether argument presence varies by a user's Brexit position and the interaction space of the comment (cross-cutting versus like-minded).For RQ3, we perform structural topic modeling on a 10% sample of the dataset to examine how the political content of Facebook comments similarly differs based on the interaction space of the comment.

Phase 1: Estimating Brexit Attitude and Charting Cross-Cutting Flows
To quantify cross-cutting comments, we sort partisans into camps based on their estimated position on the Brexit referendum.Prior research has estimated political ideology using Facebook Likes to politicians' Facebook pages (Bond & Messing, 2015) but in the "static" sense of pages outlined above.That is, Bond and Messing's (2015) study measured Likes at the page-level (i.e., subscriptions to the pages' content).Our Brexit attitude estimation focuses on reactions (Likes and Loves) at the post-level.The benefit of focusing on post reactions is that we include a prediction for users who have not subscribed to a page but still interacted with a page's posts through incidental exposure in their Feed (i.e., pages in the "dynamic" sense).We reason that liking or loving a post from a partisan Facebook page signals support for a political issue mentioned in the post and/or support for the page owners' political agenda.
We therefore estimate each user's position on the referendum as the ratio of their Likes and Loves to pro-Leave pages (VoteLeave and LeaveEU) relative to their Likes and Loves to the pro-Remain page (StrongerIn).We calculate the "Brexit Attitude Score" for each user as: The Brexit Attitude Score (BA_Score) provides a continuous measure for each user's position on the referendum between −1 (pro-Remain) and 1 (pro-Leave).If a user commented on posts but did not leave any reactions, we cannot estimate that user's position and therefore categorize the user as "Unknown."Similarly, a user who equally Liked or Loved posts from both types of pages (resulting in a BA_Score of 0) is classified as Unknown, since we cannot infer their leaning.Only 587 users (0.2%) were of this latter Unknown type; thus, we do not consider conflating these Unknowns with non-reacting Unknowns problematic for our results.
Our Brexit Attitude Score is an overall positivity measure.It does not include negativity using the "Angry" reaction, since the Reactions feature was rolled out during our timeframe of study (on February 24, 2016).Therefore, we cannot be confident that using Angry to signal disapproval had become a shared norm among users.Moreover, we find that Angry is not only a reaction issued to counter-attitudinal pages.Often, posts from a pro-Leave page would elicit Angry reactions from pro-Leave users if the post's intent was to attack Remain opponents.
We validated our Brexit Attitude Score with manual coding, where we classified users' position on the referendum based on their self-expressed voting intent or stated position on the EU through the content of their comments.We detail this validation procedure at length in the Appendix.However, it is worth noting here that especially for the Unknown category, some users could be classified differently based on our manual classifications (using comment content) and the automated method (using reactions).This is because some users would state their Brexit position in comments but leave no reactions.Conversely, some users showed a clear attitude toward Brexit through their reactions, but did not explicitly state this position in comments.Given this quirk in classifying Unknowns, reporting intercoder reliability across the two methods would be misleading low.Instead, we report that comparing the classifications of cross-cutting comments for all position-types (Brexiteer, Remainer, and Unknown) across the two methods yields a Krippendorff's alpha of .89,and the manual coding did not provide a significant classification advantage over the automated method (see Appendix, pp.[3][4][5]. Once each user was assigned a Brexit Attitude Score, comments could then be classified as one of seven "Comment Types."Cross-Cutting Comments refer to comments on the counter-attitudinal page (e.g., a Brexiteer comment to a StrongerIn post).Like-Minded Comments refer to comments on the attitude-congruent page (e.g., a Brexiteer comment to a VoteLeave or LeaveEU post).Unknown Comments refer to comments from users whose Brexit Attitude could not be inferred.For each of these three comment types, we further distinguish whether the comment is First Order (not embedded as a reply) or Second Order (a reply to another comment).Therefore, each category -Cross-Cutting, Like-Minded, and Unknown -can either be first or second order, resulting in six comments types (Cross-Cutting First Order, Cross-Cutting Second Order, etc.).
During our analysis, we uncovered the need to distinguish a seventh comment type, which we call Cross-Cutting Counter-Replies.A Counter-Reply is a comment to one's likeminded page but in reply to a Cross-Cutting Comment (and is therefore always second order).For example, if a Remainer commented on a StrongerIn post, but in reply to a Brexiteer's cross-cutting comment, this would be a cross-cutting counter-reply (since the Remainer "counters" the incoming cross-cutting comment with a "reply" on their own page).Conceptually, we consider Counter-Replies a form of cross-cutting expression, since the incursion of an opponent into one's "home turf" opens up a counter-attitudinal space at the level of comment threads.As we shall see, nuancing counter-attitudinal spaces to the thread level becomes necessary, since Facebook users are not constrained to commenting solely within like-minded spaces.

Phase 2: Classifying Reasoned Political Arguments
To examine the relationship between cross-cutting comments and reasoned political arguments, we took a random sample of 5,000 comments 3 and manually coded for the presence of reasoned political arguments.We operationalized reasoned political arguments as fulfilling all of the following criteria: were about Brexit or a related political issue; made a claim about that issue; and justified that claim with a fact, personal example, or logic.This coding scheme is derived from two existing codes from deliberative theory.The first is Stromer-Galley's (2007, p. 4) Reasoned Opinion Expression, defined as assertions "grounded in empirically verifiable evidence or in shared understanding of moral or normative behavior."For the purposes of our coding, we do not consider the veracity of facts.Instead, we treat "facts" as claims presented with evidence that is empirically verifiable, but we do not fact-check every claim ourselves.We take this decision to minimize researcher bias in assessing what users present as factual, for example regarding their lived experiences which we cannot verify.Therefore, our operationalization captures reasoning on the part of the user, rather than judgments about what we consider to be factual or reasonable.
The second code we borrow from is Halpern andGibbs' (2013, p. 1163) Type of Argumentation, which concerns "the use of logic and reasoning by individuals."Logic could include hypothetical scenarios and is especially important for justifying futureoriented claims, where facts are not yet available.Our codebook with anonymized examples is provided in the Appendix (pp.[7][8].After several rounds of coding between two of the authors on redrawn samples of 100 comments, we reached sufficient levels of intercoder reliability (Krippendorf's alpha = .81).When coding the full 5,000 comment sample, edge cases were flagged and discussed to arrive at mutually agreed upon codes.To explore associations between Reasoned Arguments (DV) and our independent variables (IVs) of interest, we then performed three binary logistic regressions.Brexit Attitude is the IV for Model 1, Comment Type is the IV for Model 2, and we test for interaction effects between Brexit Attitude and Comment Type in Model 3.

Phase 3: Structural Topic Models
To explore the relationship between political topics and cross-cutting expression (RQ3), we performed structural topic modeling (STM) on a 10% sample of the dataset using the stm package in R (Roberts et al., 2019).Structural topic modeling is an unsupervised content analysis method that clusters texts based on word co-occurrences within and across documents (in our case, Facebook comments).A key benefit of STMs is that they support the inclusion of researcher-specified covariates, which can be used to correlate the relationship between these covariates and the prevalence of a given topic.We included four covariates in our STM: Brexit Attitude, Comment Type, Date, and a variable we refer to as Chain Comments.Chain Comments, discussed in further detail below, refer to long-form comments that are clearly copied and pasted by users.Since topic models group comments based on word co-occurrences, Chain Comments will lead to topic overfitting.Thus, we use partial string matching to classify Chain Comments and include them as a covariate in the STM to distinguish between topics influenced by Chain Comments versus primarily "organic" ones (i.e., original, user-generated content).
A full detailing of our topic modeling and labeling procedure is in the Appendix.Once we arrived at our final model of 29 topics, we performed linear regressions correlating topic prevalence with our three main covariates of interest (Brexit Attitude, Comment Type, and Chain Comment).If the topic showed a strongly significant relationship with Comment Type and Chain Comment (p-value < .001),we retained the topic and plotted it in a twodimensional vector space.We decided to keep topics that did not significantly correlate with Brexit Attitude, since these would indicate issues discussed evenly by both sides.This will become clearer when we present Figure 5. Now, we turn first to our descriptive overview of the dataset.

Descriptive Overview
Figure 1 depicts the overall number of posts by campaign Facebook page, as well as the number of unique commenters and comments by their estimated Brexit Attitude Score.Moving from left to right, the left-most bar chart shows the breakdown of posts issued by the three campaign pages from February 4 -August 31, 2016. 4The unofficial LeaveEU page issued 1,029 posts, whereas StrongerIn and VoteLeave issued 408 and 541 posts, respectively.
The middle chart in Figure 1 depicts the number of unique commenters per page, colored by Brexit Attitude Score (red = pro-Leave, blue = pro-Remain, and gray = Unknown).In total, there are 344,844 unique users in our dataset; however, they could comment on posts from multiple pages and therefore be double-counted.The number of users who commented on both VoteLeave and LeaveEU posts was quite high: 50,706 (15% of users).This overlap helps justify grouping users positively reacting to both pro-Leave pages as a single category of "Brexiteers." We assigned each user a Brexit Attitude Score based on their reaction activity.We estimate that 38,226 users leaned Remain (11%), 187,239 users leaned Leave (54%), and the remaining 35% were classified as Unknown (since they did not react to any posts).The right-most chart in Figure 1 depicts the overall number of comments per page.Here, we see that Unknown users, while comprising one-third of users, left only 12% of comments.By contrast, Brexiteers left the vast majority of comments (72%) compared to Remainers (16%).
Taken together, three results emerge from Figure 1.First, the LeaveEU campaign is most active by all three metrics: page posts, unique users commenting to those posts, and overall comments per page.Second, Unknown users are much more represented in the unique number of users (35%) than in the overall number of comments (12%).Third, while Brexiteers left the most comments by far, cross-cutting comments are still present on each of the three pages.

Cross-Cutting Expression Measured Through Comments
To quantity and chart the directional flow of cross-cutting comments, we now turn to answering RQ1: To what extent does cross-cutting expression occur in Facebook comments?Figure 2 depicts the directional flow of all comments in our dataset from the estimated Brexit Attitude Score of the user (left) to the page that issued the post (right).Here, the color purple 5 depicts cross-cutting comments, meaning that the comment was left on the opposing partisan page from the user's Brexit position.The color blue signifies cross-cutting counter-replies, which are comments on the ideological home page but in reply to a cross-cutting comment from an opponent.Comments in yellow indicate that the comment is like-minded, i.e., that the user commented on the page aligned with their Brexit position.In gray, we include Unknown users' comments, to show their proportion in the dataset.
Overall, we identified 484,274 cross-cutting comments (22% of the comments in our data).An additional 153,714 comments (7%) were cross-cutting counter-replies.Since we consider counter-replies to be a form of cross-cutting expression, our answer to RQ1 is that 29% of the Facebook comments in our data are cross-cutting.Viewed as raw numbers, the vast majority of cross-cutting comments flowed from pro-Brexit users to the StrongerIn page (411,072 or 64%).In fact, Brexiteers were so active in cross-cutting expression that they left over half (51%) of the comments to StrongerIn's posts.When Remainers did engage in cross-cutting expression, it primarily took the form of counter-replies to the Brexiteer incursion on the StrongerIn page.The lower right-hand corner of Figure 2 shows that the overall breakdown of comments to the StrongerIn page left little room for like-minded discussions: 51% of comments were issued by Brexiteers, 16% were counter-replies to these cross-cutting comments, and 14% were unclassifiable (Unknown).Thus, only 19% of comments on the StrongerIn page were posted by Remainers in way that signifies like-minded discussion.
Conversely, we find that both pro-Brexit pages enjoyed comparatively high levels of likeminded comments (79% for VoteLeave and 84% for LeaveEU).However, this is not to say that Remainers did not engage in cross-cutting expression to pro-Brexit pages.If we analyze cross-cutting comments proportionately per Brexit position, 20% of Remainers' comments were issued to VoteLeave or LeaveEU, whereas 26% of Leavers' comments were issued to StrongerIn.Thus, users from both sides engaged in cross-cutting expression at proportionate levels; it is rather the sheer volume of Brexiteers' comments that skews the raw numbers on aggregate.
From this presentation of the data, three follow-up questions arise that require clarification.First, are the levels of cross-cutting expression we find concentrated around specific time points, such as the voting day?If so, this would signal that cross-cutting expression is eventdriven and not a common feature of social media behavior.Second, is the number of crosscutting comments attributable to only a handful of users?If so, reporting only raw numbers would misrepresent cross-cutting as general phenomenon when it might be attributable to a few users.Third, what is the level of "spam" in these comments?If we find the majority of cross-cutting comments are non-organic, this would limit the meaningfulness of crosscutting expression for political discussions on social media.We address the longitudinal question first.
Figure 3 depicts a time series of the data by campaign page and by comment type. 6 Succinctly put, we find that Brexiteers' cross-cutting expression to the StrongerIn page was sustained before, during, and after the campaign period.By contrast, Remainers' crosscutting activity rose with proximity to the vote, but the number of Remainers' cross-cutting comments pales in comparison to Brexiteers' like-minded comments on both pro-Leave pages.
Turning to the question of user activity, we find a power law distribution for the number of comments per user: 55% of users left only one comment and an additional 20% left two comments.In other words, 75% of users left less than three comments in the entire 30-week period.As is often the case with social media studies, a small number of users left the vast majority of comments.Importantly, however, we do not find drastic differences in this user activity distribution across Brexit attitudes or comment types.Figure 4 presents a boxplot of the median comments per user by ideology and comment type, which is somewhat crude given the activity skew in our dataset.Note that a base−10 log transformation is applied to the y-axis in order to accommodate these outliers, which we include to show that they are present across all comment types.
The median comments per user is only 1 or 2 for all comment types.Therefore, it is indeed the case that a small number of users are responsible for the majority of cross-cutting comments.Yet, a small number of users are also responsible for most like-minded comments, too. Figure 4 shows similar patterns in the commenting distributions across Brexit attitudes and comment types.The clearest difference is in Cross-Cutting Counter-Replies, where Remainers were much more active in responding to Brexiteers.
As the outliers in Figure 4 reveal, each side of the Brexit referendum had extremely prolific users.This begs the question: what percentage of comments could be considered spam?Here, we prefer the term "Chain Comments" over "Spam," since spam entails the inclusion of a hyperlink and connotes a malicious social engineering intent.By contrast, the repetitive posts in our data are more like "chain letters," with the intent of forwarding information onwards.Chain comments included, for example, listicles of reasons to vote Leave or companies that closed factories in the UK to pursue operations elsewhere.Since users often added their own text to these chain comments or altered punctuation (presumably to avoid content moderation filters), we could not simply deduplicate comments by their content.Instead, we detect chain comments by identifying the median 50 strings of comments over 150 characters and attempting to match these string concatenations against all other comments in the dataset. 7Manual checks showed that this measure performed sufficiently well to categorize long-form posts that were clearly copied and pasted.We estimate 2.8% of comments were Chain Comments (3.4% from Brexiteers, 1.2% from Remainers, and 1% from Unknowns).In sum, our descriptive reporting reveals four top-line findings.First, a substantial proportion of comments on Facebook are cross-cutting (29%).Second, cross-cutting expression is not constrained to user ideology; we find both Brexiteers and Remainers engage in cross-cutting expression at proportionate levels.Third, when viewed in raw numbers, we find pro-Brexit users were much more active in commenting, to such an extent that their comments outnumber pro-Remain users on the StrongerIn page.Fourth, we discount the possibility that the majority of cross-cutting comments are "spam," with 97% of comments in the data being organic, user-generated content.

Reasoned Political Arguments
We manually coded reasoned political arguments to provide a narrow, content-based measure of cross-cutting to counter-balance our broad, context-based operationalization.Our random sample of 5,000 comments was issued by 4,199 unique users.Since a randomly chosen comment is likely to be generated by a high commenting user, the users in our sample are disproportionately active and generated ¼ of the comments in the dataset.We consider this a beneficial bias, since we oversample for active users in the Brexit conversation.
Overall, our coding identified 342 comments containing reasoned political arguments (7% of the sample).Before running logistic regressions to test the relationship between Reasoned Arguments (DV), Brexit Attitude (IV), and Comment Type (IV), we performed Pearson's chi-square tests of independence for the two IVs.Results showed that Brexit Attitude and Comment Type are not independent of one another (χ2 = 1103, df = 4, p-value <.001).Therefore, we report odds ratios instead of coefficients in Table 3. Model 1 tests for relationships between Reasoned Arguments and Brexit Attitude.Model 2 tests relationships between Reasoned Arguments and Comment Types.Model 3 tests for an interaction term for Brexit Attitude and Comment Type.All models exclude Unknown users, but our results do not change with their inclusion. 8 Model 1 suggests that relative to Brexiteers, Remainers were slightly more likely to include reasoned arguments about Brexit in their Facebook comments.However, recall that due to the influx of Brexiteer comments on the StrongerIn page, Remainers' comments were often in reply to Brexiteers' cross-cutting comments (i.e., counter-replies).We therefore include Comment Types as IVs in Model 2, in order to examine whether the space of interaction (cross-cutting or like-minded) has stronger associations with argument presence than ideology alone.Indeed, Model 2 supports this notion.Relative to like-minded first order comments (the reference category), all three forms of cross-cutting expression are strongly associated with reasoned arguments.Furthermore, Model 3 shows that none of the interactions between Brexit Attitude and Comment Type are significant.To us, these results suggest that political priors like ideology are less associated with arguments than with a cross-cutting space of interaction.

Political Topics in the Facebook Brexit Conversation
To answer RQ3, regarding cross-cutting expression and its relation to comment content, we plotted the results of our STMs in Figure 5.The values on the axes represent the coefficients of our linear models regressing topic prevalence against Brexit Attitude, Comment Type, and Chain Comments.We report Brexit Attitude on the x-axis, Comment Type on the y-axis, and indicate the degree to which a topic included Chain Comments through a color gradient.For the x-axis, negative values (left) are topics associated with a pro-Remain attitude, and positive values (right) are topics associated with a pro-Brexit Attitude.Along the y-axis, positive values (top) are more likely to be cross-cutting, whereas negative values (bottom) are more likely to be like-minded.Topic labels shaded grey are populated by Chain Comments, whereas labels in black are predominantly organic.
In addition, our coding of arguments provides extra richness with a fourth variable, Arguments, which we calculated using theta values from our STM models (i.e., posterior probability distributions) and is indicated by point size.The size of points provides an overview of what topics Facebook users were making reasoned arguments about, as well as whether they were more likely to appear in cross-cutting versus like-minded spaces.We report the full distribution of arguments by topic in the Appendix.
Corroborating the results of our logistic regressions, we find that topics more likely to be cross-cutting (top-half) contained more political arguments than like-minded topics (bottom-half).These arguments were mostly concentrated around discussions of trade, the cost of immigration, and EU democracy.Topics containing arguments feature quite centrally on the x-axis, indicating that both Remainers and Brexiteers were active in discussing them (e.g., the EU's economic crisis, the corrosion of national industry, and public services being stressed by migration).Interestingly, the cross-cutting topic most associated with Remainers was their lamenting of Brexiteers' "Poor Facts and Bad Sources."The topic most aligned with Brexiteers' cross-cutting comments was spamming links promoting "LeaveEU Campaign Videos."Perhaps our most consequential finding relates to like-minded spaces rather than crosscutting ones.We find that no topics were associated with Remainers' like-minded discussions (bottom-left quadrant).This suggests that pro-Remain users had no opportunity to discuss political issues unimpeded by Brexiteers' cross-cutting expressions.By contrast, we find 12 topics that Brexiteers were able to discuss on their like-minded pages, and we categorize these topics into three groups: political discussion, community building, and political mobilization.
Brexiteers' political discussions included their picks for the next British Prime Minister (Next PM), commenting on news stories and televised debates (TV Commentary), and discussions about Domestic Party Politics.We also find topics that indicate a sense of community-building within the page, such as: exhibiting laughter, insulting Remain figureheads, framing the referendum as a battle of the working class, and aligning the Brexit movement with a fight against tyranny akin to World War II.A cartesian plane depicting the topics of the topic models.The location of the topics is determined by whether they are more likely to be discussed by Remainers or Leavers (x-axis) and whether they are more likely to be cross-cutting or like-minded (y-axis).The main result is that no topic is shown in the quadrant that is pro-Remain and like-minded.Other results are reported more thoroughly in the text.
Importantly, we find three topics indicating political mobilization in the Brexiteer likeminded space.The first is "Vote with Pen," which urged others to use a black pen when voting to ensure that their votes could not be manipulated.The second mobilization topic calls for collective action to return a pro-Remain leaflet mailed to British voters by the government, in order to protest the use of public money to support the Remain cause.Third was the more general "Vote Leave (Mobilization)" topic, which was the most prevalent topic in the data and simply expressed one's desire to leave the EU -even if not accompanied by a reasoned political argument.While we find examples of Chain Comments in Brexiteers' like-minded spaces (such as the Bilderberg Group conspiracy), topics discussing political issues, exhibiting community bonding, and calling for political mobilization were predominantly organic (i.e., shaded black).
Viewed holistically, and somewhat paradoxically, we argue that the core finding of Figure 5 does not lie in our original focus on cross-cutting expression.Rather, the main takeaway of our topic models is the implication of cross-cutting expression for like-minded spaces.Our analysis shows that due to Brexiteers' cross-cutting expression, no topic wasor arguably could be -discussed by Remainers in an echo chamber.By contrast, the low rate of cross-cutting expression from Remainers allowed Brexiteers to utilize the VoteLeave and LeaveEU Facebook pages as spaces for political discussion, community building, and mobilization.Thus, we argue that the unidirectional cross-cutting patterns we observe effectively disarmed the utility of the StrongerIn page for political mobilization, a notion we further unpack in concluding the study.

Discussion and Conclusion
To complement survey research studying cross-cutting interactions on social media (Chan et al., 2021;Kwak et al., 2020;Lu & Lee, 2020), we shifted our focus from exposure to expression and operationalized our theoretical arguments with digital trace data.We defined cross-cutting expression as users' acts of political communication through speech or behavior within a counter-attitudinal space.Crucially, this conceptualization goes beyond the articulation of verbal political opinions to also include expressive practices in digital spaces.Social media users "crossing-over" into online partisan spaces, even without the primary purpose of engaging in thoughtful deliberation, can constitute meaningful acts of digital presence that existing content-based operationalizations of cross-cutting do not capture.
To buttress this argument, we first answer RQ1, which asked: To what extent does crosscutting expression occur in Facebook comments?From our dataset of 2 million Facebook comments to three political campaign pages during the Brexit Referendum, we estimate that 29% of comments were cross-cutting.In raw numbers, the vast majority of these crosscutting comments (and indeed, comments overall) were issued by pro-Brexit users.However, when viewed proportionately, a comment from a pro-Brexit and pro-Remain user were similarly likely to be cross-cutting (26% and 20%, respectively).Still, the uneven distribution of commenting by Brexiteers supports prior research that users voicing challenger and nationalist positions are most active on Twitter (Dutceac Segesten & Bossetta, 2017) and, more broadly, that user activity on political Facebook pages follows a power law distribution where most users exhibit low engagement activity (Nielsen & Vaccari, 2013).One theoretical explanation for this user activity skew is Facebook's digital architecture and, more specifically, the dual character of Facebook pages.Facebook pages are simultaneously designed as static spaces that users can navigate to on the platform, as well as dynamic constructs that appear ephemerally in users' Feeds.We posit that the dynamic character of Facebook pages creates incidental exposure at the post-level, which may provoke users to comment on a single post but not necessarily visit the static page on a regular basis.Meanwhile, a smaller group of politically-motivated users may consistently navigate to the static page and comment on multiple posts, where the Facebook interface displays posts in reverse chronological order.We cannot determine from our data whether a comment was left on a static page or a dynamically-inserted post; however, purposeful commenting to static pages likely explains some, if not most, of the imbalance in commenting activity we find.
Second, we asked RQ2: What is the relationship between cross-cutting expression and reasoned political arguments?We have argued that cross-cutting expression is a contextdependent activity that is not constrained exclusively to content -namely, the verbalized exchange of political views.Therefore, RQ2 distinguishes between the act of cross-cutting expression and content-based measures of opinion justification.Moreover, we consider reasoned political arguments to comprise "high quality" discourse amidst the trove of noise in Facebook comments, and therefore RQ2 provides a rough approximation of the "deliberative quality" of Facebook comments at a substantive (rather than normative) level of opinion exchange.
We found that only 7% of comments contained a reasoned political argument.In our models, arguments were more strongly associated with the clash of ideologies at the space of interaction, vis-à-vis one's Brexit position per se.We interpret these results to suggest that the context of a digital space matters for reasoned arguments appearing in social media discourse.While other studies demonstrate that disagreement (a content-based measure) correlates with opinion justification (another content-based measure) in Facebook comments (Rossini, 2022), we show that such justifications can also be explained with context-based measures largely independent of content -namely, the ideological distance between user and page (cross-cutting first order comments) as well as between ideologically opposed users independent of page location (cross-cutting second order comments and counter-replies).
Although we did not directly measure disagreement, our focus on arguments provokes the question of what studies may overlook by overfitting research designs to search for deliberation on social media.The fact that we identified 29% of comments as cross-cutting based on context, while only 7% of comments contained arguments based on content, raises concerns about the potential limitations of research aiming to measure deliberation in online spaces.If we had solely concentrated on the deliberative quality of Facebook comments, we may have concluded that Facebook is not a deliberative space given the low occurrence of arguments.Alternatively, we could have focused our analysis on deliberation's death knell -incivility -to argue that Facebook comments in a polarized climate do not meet the ideal type standards from political theory.However, we chose not to focus on incivility since it currently lacks a clearly operationalizable negation (Sartori, 1970).Therefore, although an important object of study, incivility remains a one-sided concept with questionable concept validity and arguably, real analytical utility beyond normative description and measurement.
Instead, our research design yields two broader insights.First, reasoned arguments on Facebook emerge when partisans choose to express themselves in cross-cutting spaces, and thus the contexts of online spaces matter.This finding holds relevance for platform developers, who could tweak their platforms' architectures to design spaces conducive to cross-partisan fertilization.Second and more importantly, our findings suggest that crosscutting expression is relevant beyond the level of content and extends also into the realm of participatory action.
In supporting this claim, RQ3 asked: What is the relationship between cross-cutting expression and political topics discussed during the Brexit debate on Facebook?Here, we find stark differences in how cross-cutting expression affected like-minded discussions.On the pro-Remain page, where over half of the comments were left by Leavers, Remainers commented as equally to their like-minded space as to threads opened up by counterattitudinal users.We interpret this dynamic to signal that Brexiteers' cross-cutting expression reduced the potential for Remainers' issue-ownership (e.g., advocating a clear, hard-torefute policy stance on why Brexit will adversely affect the UK) as well as the political organization potential of the StrongerIn page.Our models show that no topic was fully "owned" by Remainers; instead, they were often on the back-foot in responding to Brexiteers.Conversely, in the absence of such ideological information interference, Brexiteers utilized their pro-Leave spaces for political discussions and crucially, to support both formal and extra-parliamentary forms of participation.Not only did Brexiteers decry the EU and discuss domestic party politics, they also consistently: reminded each other of the voting day and how to register; called for voting with a black pen to ensure their vote was not manipulated; and collectively protested government-sponsored leaflets by posting them back to Number 10.
Succinctly put, we argue that Brexiteers' incursion into the StrongerIn page disarmed its potential for political organization.Individual acts of cross-cutting expression may not be the only contributor of this disarmament but rather, a more collective acknowledgment by Remainers that the StrongerIn page had been hijacked.During our manual coding, we found several comments by Remainers calling for pro-Leave users to go back to their own pages or admonishing other Remainers to ignore the "Brexit trolls."The awareness that some Brexiteers were actively monitoring and engaging in StrongerIn discussions may have disincentivized some would-be Remain activists from commenting.This leads us to posit that in addition to individual acts of cross-cutting expression, Brexiteers' collective commenting practices engendered an aura of digital presence that may have affected the content, activity, and ultimate political utility of the StrongerIn page.
A direct test of the impact of such digital presence perceptions is not possible with the research undertaken here, which is limited by focusing on only one arena of the Brexit debate: three political pages that likely hosted relatively niche, politically-interested users.Yet despite this limitation, our case study contributes to the online political communication literature in three key ways.First, we show that Facebook pages are spaces for cross-cutting expression.Second, we demonstrate that cross-cutting spaces on social media correlate strongly with the presence of political arguments.Third, our reconceptualization of crosscutting expression may explain content differences in political discussions and the prospects of Facebook pages for voter mobilization.
Future research should strive to uncover whether the levels of cross-cutting expression we find are a general feature of political talk on Facebook or instead, are limited to bipolar electoral contests such as plebiscites or elections in two-party systems.Further, we strongly urge scholars to conceptualize Facebook pages as dynamic cross-cutting spaces, rather than archaic "fan pages" populated by like-minded communities.This latter assumption neglects the dynamicity of political communication on social media and perpetuates the myth of the social media echo chamber.

Notes
((Likes + Loves to posts from pro-Leave Pages) -(Likes + Loves to posts from Pro-Remain Page)) ((Likes + Loves to posts from pro-Leave Pages) + (Likes + Loves to posts from Pro-Remain Page))

Figure 1 .
Figure 1.Three bar charts reporting the number of posts, users, and comments for the three Facebook pages.The LeaveEU page has the highest values for each metric.

Figure 2 .
Figure 2.An alluvial plot of all comments in the dataset.The left side labels each comment by the Brexit attitude of the user, and the right side shows the page where the comment was issued.Colored lines between the two sides show the flow of comments from Brexit attitude to the pages.The lines are colored by comment type.The plot shows the high commenting activity of pro-Brexit users and the substantial proportion of cross-cutting comments in the dataset.Most comments flowed from pro-Brexit users to the pro-Remain page.

Figure 3 .
Figure 3. Three time series bar charts of all comments in the dataset.There is one chart for each Facebook page.The comments are colored by comment type, showing the breakdown of comment types per day.All the charts show a spike in activity around the Brexit vote.The charts show that Brexiteers cross-cutting expression occurred on the Stronger in page during the entire campaign.Much less cross-cutting expression from Remainers is shown on the pro-Brexit pages.

Figure 4 .
Figure 4. Boxplots showing comments per user by brexit attitude and comment type.There are 10 boxplots to compare the two Brexit Attitudes for each of the five comment types.The boxplots show little variation in the average number of comments per user or the existence of high commenting outliers.

Figure 5 .
Figure5.A cartesian plane depicting the topics of the topic models.The location of the topics is determined by whether they are more likely to be discussed by Remainers or Leavers (x-axis) and whether they are more likely to be cross-cutting or like-minded (y-axis).The main result is that no topic is shown in the quadrant that is pro-Remain and like-minded.Other results are reported more thoroughly in the text.
Table 1 reports results by Brexit Attitude, and Table 2 reports them by Comment Type.

Table 1 .
Descriptive overview of sample coding results by brexit attitude.

Table 2 .
Descriptive overview of sample coding results by comment type.