Most previous analysis of Twitter user behavior is focused on individual information cascades and the social followers graph. We instead study aggregate user behavior and the retweet graph with a focus on quantitative descriptions. We find that the lifetime tweet distribution is a type-II discrete Weibull stemming from a power law hazard function, the tweet rate distribution, although asymptotically power law, exhibits a lognormal cutoff over finite sample intervals, and the inter-tweet interval distribution is power law with exponential cutoff. The retweet graph is small-world and scale-free, like the social graph, but is less disassortative and has much stronger clustering. These differences are consistent with it better capturing the real-world social relationships of and trust between users. Beyond just understanding and modeling human communication patterns and social networks, applications for alternative, decentralized microblogging systems-both predicting real-word performance and detecting spam-are discussed.
There has been much effort on studying how social media sites, such as Twitter, help propagate information in different situations, including spreading alerts and SOS messages in an emergency. However, existing work has not addressed how to actively identify and engage the right strangers at the right time on social media to help effectively propagate intended information within a desired time frame. To address this problem, we have developed two models: (i) a feature-based model that leverages peoples' exhibited social behavior, including the content of their tweets and social interactions, t…
In this paper we model user behaviour in Twitter to capture the emergence of trending topics. For this purpose, we first extensively analyse tweet datasets of several different events. In particular, for these datasets, we construct and investigate the retweet graphs. We find that the retweet graph for a trending topic has a relatively dense largest connected component (LCC). Next, based on the insights obtained from the analyses of the datasets, we design a mathematical model that describes the evolution of a retweet graph by three main parameters. We then quantify, analytically and by simula…
Complex networks often exhibit co-evolutionary dynamics, meaning that the network topology and the state of nodes or links are coupled, affecting each other in overlapping time scales. We focus on the co-evolutionary dynamics of online social networks, and on Twitter in particular. Monitoring the activity of thousands of Twitter users in real-time, and tracking their followers and tweets/retweets, we propose a method to infer new retweet-driven follower relations. The formation of such relations is much more likely than the exogenous creation of new followers in the absence of any retweets. We…
In modern election campaigns, political parties utilize social media to advertise their policies and candidates and to communicate to the electorate. In Japan's latest general election in 2017, the 48th general election for the Lower House, social media, especially Twitter, was actively used. In this paper, we analyze the users who retweeted tweets of political parties on Twitter during the election. Our aim is to clarify what kinds of users are diffusing (retweeting) tweets of political parties. The results indicate that the characteristics of retweeters of the largest ruling party (Liberal D…
We study the evolution of the number of retweets received by Twitter users over the course of their "careers" on the platform. We find that on average the number of retweets received by users tends to increase over time. This is partly expected because users tend to gradually accumulate followers. Normalizing by the number of followers, however, reveals that the relative, per-follower retweet rate tends to be non-monotonic, maximized at a "peak age" after which it does not increase, or even decreases. We develop a simple mathematical model of the process behind this phenomenon, which assumes a…
The past decade has witnessed a marked increase in the use of social media by politicians, most notably exemplified by the 45th President of the United States (POTUS), Donald Trump. On Twitter, POTUS messages consistently attract high levels of engagement as measured by likes, retweets, and replies. Here, we quantify the balance of these activities, also known as "ratios", and study their dynamics as a proxy for collective political engagement in response to presidential communications. We find that raw activity counts increase during the period leading up to the 2016 election, accompanied by …
We present a hierarchical model of non-homogeneous Poisson processes (NHPP) for information diffusion on online social media, in particular Twitter retweets. The retweets of each original tweet are modelled by a NHPP, for which the intensity function is a product of time-decaying components and another component that depends on the follower count of the original tweet author. The latter allows us to explain or predict the ultimate retweet count by a network centrality-related covariate. The inference algorithm enables the Bayes factor to be computed, in order to facilitate model selection. Fin…
Twitter is used for a variety of reasons, including information dissemination, marketing, political organizing and to spread propaganda, spamming, promotion, conversations, and so on. Characterizing these activities and categorizing associated user generated content is a challenging task. We present a information-theoretic approach to classification of user activity on Twitter. We focus on tweets that contain embedded URLs and study their collective `retweeting' dynamics. We identify two features, time-interval and user entropy, which we use to classify retweeting activity. We achieve good sep…
Most studies on social influence have focused on direct influence, while another interesting question can be raised as whether indirect influence exists between two users who're not directly connected in the network and what affects such influence. In addition, the theory of \emph{complex contagion} tells us that more spreaders will enhance the indirect influence between two users. Our observation of intensity of indirect influence, propagated by $n$ parallel spreaders and quantified by retweeting probability on Twitter, shows that complex contagion is validated globally but is violated locall…
Based on the definition of the well-known h index we propose a t factor for measuring the impact of publications (and other entities) on Twitter. The new index combines tweet and retweet data in a balanced way whereby retweets are seen as data reflecting the impact of initial tweets. The t factor is defined as follows: A unit (single publication, journal, researcher, research group etc.) has factor t if t of its Nt tweets have at least t retweets each and the other (Nt-t) tweets have <=t retweets each.
Celebrity endorsements are often sought to influence public opinion. We ask whether celebrity endorsement per se has an effect beyond the fact that their statements are seen by many, and whether on net their statements actually lead people to change their beliefs. To do so, we conducted a nationwide Twitter experiment in Indonesia with 46 high-profile celebrities and organizations, with a total of 7.8 million followers, who agreed to let us randomly tweet or retweet content promoting immunization from their accounts. Our design exploits the structure of what information is passed on along a re…
IIT-CNR（意大利国家研究委员会信息技术研究所）；University of Pisa（比萨大学）；Ca’ Foscari University of Venice（威尼斯卡福斯卡里大学）
Within OSNs, many of our supposedly online friends may instead be fake accounts called social bots, part of large groups that purposely re-share targeted content. Here, we study retweeting behaviors on Twitter, with the ultimate goal of detecting retweeting social bots. We collect a dataset of 10M retweets. We design a novel visualization that we leverage to highlight benign and malicious patterns of retweeting activity. In this way, we uncover a 'normal' retweeting pattern that is peculiar of human-operated accounts, and 3 suspicious patterns related to bot activities. Then, we propose a bot …
Online social networking services allow their users to post content in the form of text, images or videos. The main mechanism driving content diffusion is the possibility for users to re-share the content posted by their social connections, which may then cascade across the system. A fundamental problem when studying information cascades is the possibility to develop sound mathematical models, whose parameters can be calibrated on empirical data, in order to predict the future course of a cascade after a window of observation. In this paper, we focus on Twitter and, in particular, on the tempo…
Serious concerns have been raised about the role of 'socialbots' in manipulating public opinion and influencing the outcome of elections by retweeting partisan content to increase its reach. Here we analyze the role and influence of socialbots on Twitter by determining how they contribute to retweet diffusions. We collect a large dataset of tweets during the 1st U.S. Presidential Debate in 2016 (#DebateNight) and we analyze its 1.5 million users from three perspectives: user influence, political behavior (partisanship and engagement) and botness. First, we define a measure of user influence ba…
Twitter is a popular microblogging platform. When users send out messages, other users have the ability to forward these messages to their own subgraph. Most research focuses on increasing retweetability from a node's perspective. Here, we center on improving message style to increase the chance of a message being forwarded. To this end, we simulate an artificial Twitter-like network with nodes deciding deterministically on retweeting a message or not. A genetic algorithm is used to optimize message composition, so that the reach of a message is increased. When analyzing the algorithm's runtim…
Twitter has been increasingly used for spreading messages about campaigns. Such campaigns try to gain followers through their Twitter accounts, influence the followers and spread messages through them. In this paper, we explore the relationship between followers sentiment towards the campaign topic and their rate of retweeting of messages generated by the campaign. Our analysis with followers of multiple social-media campaigns found statistical significant correlations between such sentiment and retweeting rate. Based on our analysis, we have conducted an online intervention study among the fo…
This article analyses public debate on Twitter via network representations of retweets and replies. We argue that tweets observable on Twitter have both a direct and mediated effect on the perception of public opinion. Through the interplay of the two networks, it is possible to identify potentially misleading representations of public opinion on the platform. The method is employed to observe public debate about two events: The Saxon state elections and violent riots in the city of Leipzig in 2019. We show that in both cases, (i) different opinion groups exhibit different propensities to get …
Retweet-BERT: Political Leaning Detection Using Language Features and Information Diffusion on Social Networks
Information Sciences Institute, University of Southern California（南加州大学信息科学研究所）；Viterbi School of Engineering, University of Southern California（南加州大学维特比工程学院）；Annenberg School of Communication, University of Southern California（南加州大学安纳伯格传播学院）
In this preliminary study we compare the characteristics of retweets and replies on more than 350,000 messages collected by following members of the German Federal Diet on Twitter. We find significant differences in the characteristics pointing to distinct types of usages for retweets and replies. Using time series and regression analysis we observe that the likelihood of a politician using replies increases with typical leisure times while retweets occur constant over time. Including formal references increases the probability of a message being retweeted but drops its chance of being replied…
In social network Twitter, users can interact with each other and spread information via retweets. These millions of interactions may result in media events whose influence goes beyond Twitter framework. In this paper, we thoroughly explore interactions to provide a better understanding of the emergence of certain trends. First, we consider an interaction on Twitter to be a triplet $(s,a,t)$ meaning that user $s$, called the spreader, has retweeted a tweet of user $a$, called the author, at time $t$. We model this set of interactions as a data cube with three dimensions: spreaders, authors and…
Boston University（波士顿大学）；University of Crete（克里特大学）
This paper investigates the interplay between different types of user interactions on Twitter, with respect to predicting missing or unseen interactions. For example, given a set of retweet interactions between Twitter users, how accurately can we predict reply interactions? Is it more difficult to predict retweet or quote interactions between a pair of accounts? Also, how important is time locality, and which features of interaction patterns are most important to enable accurate prediction of specific Twitter interactions? Our empirical study of Twitter interactions contributes initial answer…
Arguably one of the most important features of Twitter is the support for "retweets" or messages re-posted verbatim by a user that were originated by someone else. (This does not include modified tweets that sometimes are referred to as retweets.) Despite the fact that retweets are routinely studied and reported, many important questions remain about user motivation for their use and their significance. In this paper we answer the question of what users indicate when they retweet. We do so in a comprehensive fashion, by employing a user survey, a study of user profiles, and a meta-analysis of …
Twitter has increasingly become a popular platform to share news and user opinion. A tweet is considered to be important if it receives high number of affirmative reactions from other Twitter users via Retweets. Retweet count is thus considered as a surrogate measure for positive crowd-sourced reactions - high number of retweets of a tweet aid in making its topic trending. This in turn bolsters the social reputation of the author of the tweet. Since social reputation/impact of users/tweets influences many decisions (such as promoting brands, advertisement etc.), several blackmarket syndicates …
We present a study to analyze how word use can predict social engagement behaviors such as replies and retweets in Twitter. We compute psycholinguistic category scores from word usage, and investigate how people with different scores exhibited different reply and retweet behaviors on Twitter. We also found psycholinguistic categories that show significant correlations with such social engagement behaviors. In addition, we have built predictive models of replies and retweets from such psycholinguistic category based features. Our experiments using a real world dataset collected from Twitter val…
Recent work has found that the propagation of behaviors and sentiments through networks extends in ranges up to 2 to 4 degrees of distance. The regularity with which the same observation is found in dissimilar phenomena has been associated with friction in the propagation process and the instability of link structure that emerges in the dynamic of social networks. We study a contagious behavior, the practice of retweeting, in a setting where neither of those restrictions is present and still found the same result.
The global public sphere has changed dramatically over the past decades: a significant part of public discourse now takes place on algorithmically driven platforms owned by a handful of private companies. Despite its growing importance, there is scant large-scale academic research on the long-term evolution of user behaviour on these platforms, because the data are often proprietary to the platforms. Here, we evaluate the individual behaviour of 600,000 Twitter users between 2012 and 2019 and find empirical evidence for an acceleration of the way Twitter is used on an individual level. This ma…
Jožef Stefan Institute（约瑟夫·斯蒂芬研究所）；Université Panthéon-Sorbonne（巴黎第一大学）；Paris School of Economics（巴黎经济学院）
We study the cohesion within and the coalitions between political groups in the Eighth European Parliament (2014--2019) by analyzing two entirely different aspects of the behavior of the Members of the European Parliament (MEPs) in the policy-making processes. On one hand, we analyze their co-voting patterns and, on the other, their retweeting behavior. We make use of two diverse datasets in the analysis. The first one is the roll-call vote dataset, where cohesion is regarded as the tendency to co-vote within a group, and a coalition is formed when the members of several groups exhibit a high …
Influential users have great potential for accelerating information dissemination and acquisition on Twitter. How to measure the influence of Twitter users has attracted significant academic and industrial attention. Existing influential measurement techniques, however, are vulnerable to sybil users that are thriving on Twitter. Although sybil defenses for online social networks have been extensively investigated, they commonly assume unique mappings from human-established trust relationships to online social associations and thus do not apply to Twitter where users can freely follow each othe…
Social media platforms provide several social interactional features. Due to the large scale reach of social media, these interactional features help enable various types of political discourse. Constructive and diversified discourse is important for sustaining healthy communities and reducing the impact of echo chambers. In this paper, we empirically examine the role of a newly introduced Twitter feature, 'quote retweets' (or 'quote RTs') in political discourse, specifically whether it has led to improved, civil, and balanced exchange. Quote RTs allow users to quote the tweet they retweet, wh…
Modern social media platforms facilitate the rapid spread of information online. Modelling phenomena such as social contagion and information diffusion are contingent upon a detailed understanding of the information-sharing processes. In Twitter, an important aspect of this occurs with retweets, where users rebroadcast the tweets of other users. To improve our understanding of how these distributions arise, we analyse the distribution of retweet times. We show that a power law with exponential cutoff provides a better fit than the power laws previously suggested. We explain this fit through th…
This paper presents a method to validate the true patrons of a brand, group, artist or any other entity on the social networking site Twitter. We analyze the trend of total number of tweets, average retweets and total number of followers for various nodes for different social and political backgrounds. We argue that average retweets to follower ratio reveals the overall value of the individual accounts and helps estimate the true to fake account ratio.
German Research Center for Artificial Intelligence (DFKI)（德国人工智能研究中心）；TU Kaiserslautern（凯泽斯劳滕工业大学）；Deakin University（迪肯大学）
COVID-19 has affected the world economy and the daily life routine of almost everyone. It has been a hot topic on social media platforms such as Twitter, Facebook, etc. These social media platforms enable users to share information with other users who can reshare this information, thus causing this information to spread. Twitter's retweet functionality allows users to share the existing content with other users without altering the original content. Analysis of social media platforms can help in detecting emergencies during pandemics that lead to taking preventive measures. One such type of a…
According to the Eurobarometer report about EU media use of May 2018, the number of European citizens who consult on-line social networks for accessing information is considerably increasing. In this work we analyze approximately $10^6$ tweets exchanged during the last Italian elections. By using an entropy-based null model discounting the activity of the users, we first identify potential political alliances within the group of verified accounts: if two verified users are retweeted more than expected by the non-verified ones, they are likely to be related. Then, we derive the users' affiliati…
Jozef Stefan Institute（约瑟夫·斯特凡研究所）；Jozef Stefan International Postgraduate School（约瑟夫·斯特凡国际研究生院）；University of Ljubljana（卢布尔雅那大学）
We address a challenging problem of identifying main sources of hate speech on Twitter. On one hand, we carefully annotate a large set of tweets for hate speech, and deploy advanced deep learning to produce high quality hate speech classification models. On the other hand, we create retweet networks, detect communities and monitor their evolution through time. This combined approach is applied to three years of Slovenian Twitter data. We report a number of interesting results. Hate speech is dominated by offensive tweets, related to political and ideological issues. The share of unacceptable t…
We set up a simple mathematical model for the dynamics of public interest in terms of media coverage and social interactions. We test the model on a series of events related to violence in the US during 2020, using the volume of tweets and retweets as a proxy of public interest, and the volume of news as a proxy of media coverage. The model succesfully fits the data and allows inferring a measure of social sensibility that correlates with human mobility data. These findings suggest the basic ingredients and mechanisms that regulate social responses capable of ignite social mobilizations.
False rumors are known to have detrimental effects on society. To prevent the spread of false rumors, social media platforms such as Twitter must detect them early. In this work, we develop a novel probabilistic mixture model that classifies true vs. false rumors based on the underlying spreading process. Specifically, our model is the first to formalize the self-exciting nature of true vs. false retweeting processes. This results in a novel mixture marked Hawkes model (MMHM). Owing to this, our model obviates the need for feature engineering; instead, it directly models the spreading process …
Technical University of Denmark（丹麦技术大学）；University of Milan（米兰大学）；Copenhagen Business School（哥本哈根商学院）
The link between affect, defined as the capacity for sentimental arousal on the part of a message, and virality, defined as the probability that it be sent along, is of significant theoretical and practical importance, e.g. for viral marketing. A quantitative study of emailing of articles from the NY Times finds a strong link between positive affect and virality, and, based on psychological theories it is concluded that this relation is universally valid. The conclusion appears to be in contrast with classic theory of diffusion in news media emphasizing negative affect as promoting propagation…
Social media have become part of modern news reporting, used by journalists to spread information and find sources, or as a news source by individuals. The quest for prominence and recognition on social media sites like Twitter can sometimes eclipse accuracy and lead to the spread of false information. As a way to study and react to this trend, we introduce {\sc TwitterTrails}, an interactive, web-based tool ({\tt twittertrails.com}) that allows users to investigate the origin and propagation characteristics of a rumor and its refutation, if any, on Twitter. Visualizations of burst activity, p…
Online hate speech, particularly over microblogging platforms like Twitter, has emerged as arguably the most severe issue of the past decade. Several countries have reported a steep rise in hate crimes infuriated by malicious hate campaigns. While the detection of hate speech is one of the emerging research areas, the generation and spread of topic-dependent hate in the information network remain under-explored. In this work, we focus on exploring user behaviour, which triggers the genesis of hate speech on Twitter and how it diffuses via retweets. We crawl a large-scale dataset of tweets, ret…
How far and how fast does information spread in social media? Researchers have recently examined a number of factors that affect information diffusion in online social networks, including: the novelty of information, users' activity levels, who they pay attention to, and how they respond to friends' recommendations. Using URLs as markers of information, we carry out a detailed study of retweeting, the primary mechanism by which information spreads on the Twitter follower graph. Our empirical study examines how users respond to an incoming stimulus, i.e., a tweet (message) from a friend, and re…
The wide spread of unfounded election fraud claims surrounding the U.S. 2020 election had resulted in undermining of trust in the election, culminating in violence inside the U.S. capitol. Under these circumstances, it is critical to understand the discussions surrounding these claims on Twitter, a major platform where the claims were disseminated. To this end, we collected and released the VoterFraud2020 dataset, a multi-modal dataset with 7.6M tweets and 25.6M retweets from 2.6M users related to voter fraud claims. To make this data immediately useful for a diverse set of research projects, …
In modern election campaigns, political parties utilize social media to advertise their policies and candidates and to communicate to electorates. In Japan's latest general election in 2017, the 48th general election for the Lower House, social media, especially Twitter, was actively used. In this paper, we perform a detailed analysis of social graphs and users who retweeted tweets of political parties during the election. Our aim is to obtain accurate information regarding the diffusion power for each party rather than just the number of followers. The results indicate that a user following a…
In modeling social interaction online, it is important to understand when people are reacting to each other. Many systems have explicit indicators of replies, such as threading in discussion forums or replies and retweets in Twitter. However, it is likely these explicit indicators capture only part of people's reactions to each other, thus, computational social science approaches that use them to infer relationships or influence are likely to miss the mark. This paper explores the problem of detecting non-explicit responses, presenting a new approach that uses tf-idf similarity between a user'…
This paper presents a quantitative study of Twitter, one of the most popular micro-blogging services, from the perspective of user influence. We crawl several datasets from the most active communities on Twitter and obtain 20.5 million user profiles, along with 420.2 million directed relations and 105 million tweets among the users. User influence scores are obtained from influence measurement services, Klout and PeerIndex. Our analysis reveals interesting findings, including non-power-law influence distribution, strong reciprocity among users in a community, the existence of homophily and hie…
Two clustering methods to determine users with similar opinions on the Covid-19 pandemic and the related public debate in Germany will be presented in this paper. We believe, they can help gaining an overview over similar-minded groups and could support the prevention of fake-news distribution. The first method uses a new approach to create a network based on retweet relationships between users and the most retweeted users, the so-called influencers. The second method extracts hashtags from users posts to create a "user feature vector" which is then clustered, using a consensus matrix based on…
We predict the popularity of short messages called tweets created in the micro-blogging site known as Twitter. We measure the popularity of a tweet by the time-series path of its retweets, which is when people forward the tweet to others. We develop a probabilistic model for the evolution of the retweets using a Bayesian approach, and form predictions using only observations on the retweet times and the local network or "graph" structure of the retweeters. We obtain good step ahead forecasts and predictions of the final total number of retweets even when only a small fraction (i.e., less than …
Polarized topics often spark discussion and debate on social media. Recent studies have shown that polarized debates have a specific clustered structure in the endorsement net- work, which indicates that users direct their endorsements mostly to ideas they already agree with. Understanding these polarized discussions and exposing social media users to content that broadens their views is of paramount importance. The contribution of this demonstration is two-fold. (i) A tool to visualize retweet networks about controversial issues on Twitter. By using our visualization, users can understand how…
Mental health challenges are thought to afflict around 10% of the global population each year, with many going untreated due to stigma and limited access to services. Here, we explore trends in words and phrases related to mental health through a collection of 1- , 2-, and 3-grams parsed from a data stream of roughly 10% of all English tweets since 2012. We examine temporal dynamics of mental health language, finding that the popularity of the phrase 'mental health' increased by nearly two orders of magnitude between 2012 and 2018. We observe that mentions of 'mental health' spike annually and…
There has been a tremendous rise in the growth of online social networks all over the world in recent years. It has facilitated users to generate a large amount of real-time content at an incessant rate, all competing with each other to attract enough attention and become popular trends. While Western online social networks such as Twitter have been well studied, the popular Chinese microblogging network Sina Weibo has had relatively lower exposure. In this paper, we analyze in detail the temporal aspect of trends and trend-setters in Sina Weibo, contrasting it with earlier observations in Twi…
This paper presents twAwler, a lightweight twitter crawler that targets language-specific communities of users. twAwler takes advantage of multiple endpoints of the twitter API to explore user relations and quickly recognize users belonging to the targetted set. It performs a complete crawl for all users, discovering many standard user relations, including the retweet graph, mention graph, reply graph, quote graph, follow graph, etc. twAwler respects all twitter policies and rate limits, while able to monitor large communities of active users. twAwler was used between August 2016 and March 201…
In this paper, we present ArCOV-19, an Arabic COVID-19 Twitter dataset that spans one year, covering the period from 27th of January 2020 till 31st of January 2021. ArCOV-19 is the first publicly-available Arabic Twitter dataset covering COVID-19 pandemic that includes about 2.7M tweets alongside the propagation networks of the most-popular subset of them (i.e., most-retweeted and -liked). The propagation networks include both retweets and conversational threads (i.e., threads of replies). ArCOV-19 is designed to enable research under several domains including natural language processing, info…
Understanding the collective reaction to individual actions is key to effectively spread information in social media. In this work we define efficiency on Twitter, as the ratio between the emergent spreading process and the activity employed by the user. We characterize this property by means of a quantitative analysis of the structural and dynamical patterns emergent from human interactions, and show it to be universal across several Twitter conversations. We found that some influential users efficiently cause remarkable collective reactions by each message sent, while the majority of users m…
Measuring and forecasting opinion trends from real-time social media is a long-standing goal of big-data analytics. Despite its importance, there has been no conclusive scientific evidence so far that social media activity can capture the opinion of the general population. Here we develop a method to infer the opinion of Twitter users regarding the candidates of the 2016 US Presidential Election by using a combination of statistical physics of complex networks and machine learning based on hashtags co-occurrence to develop an in-domain training set approaching 1 million tweets. We investigate …
We address the problem of maximizing user engagement with content (in the form of like, reply, retweet, and retweet with comments)on the Twitter platform. We formulate the engagement forecasting task as a multi-label classification problem that captures choice behavior on an unsupervised clustering of tweet-topics. We propose a neural network architecture that incorporates user engagement history and predicts choice conditional on this context. We study the impact of recommend-ing tweets on engagement outcomes by solving an appropriately defined sweet optimization problem based on the proposed…
In this paper, we study the implications of the commonplace assumption that most social media studies make with respect to the nature of message shares (such as retweets) as a predominantly positive interaction. By analyzing two large longitudinal Brazilian Twitter datasets containing 5 years of conversations on two polarizing topics - Politics and Sports - we empirically demonstrate that groups holding antagonistic views can actually retweet each other more often than they retweet other groups. We show that assuming retweets as endorsement interactions can lead to misleading conclusions with …
