RESTRICTING THE SPREAD OF FIRESTORMSIN SOCIAL …...RESTRICTING THE SPREAD OF FIRESTORMS IN SOCIAL...

Twenty Second European Conference on Information Systems, Tel Aviv 2014 1

RESTRICTING THE SPREAD OF FIRESTORMS IN SOCIAL NETWORKS

Complete Research

Mochalova, Anastasia, Katholische Universität Eichstätt-Ingolstadt, Auf der Schanz 49, 85049 Ingolstadt, Germany, [email protected]

Nanopoulos, Alexandros, Katholische Universität Eichstätt-Ingolstadt, Auf der Schanz 49, 85049 Ingolstadt, Germany, [email protected]

Abstract We investigate the social-media phenomenon defined as “online firestorms”: sudden discharges of large quantities of negative word-of-mouth that spreads rapidly through online social networks. Firestorms can start due to various reasons, such as online marketing campaigns that backfired or dissatisfaction of customers, and are a consequence of opening social media channels to the crowds. Firestorms have affective and viral nature and therefore posing severe threats, such as harming brand reputation and causing customer losses.

Our motivation in this paper is the development of optimized forms of counteraction to firestorms, which engage individuals to act as supporters and initiate the spread of positive word-of-mouth, helping to constrain the firestorm as much as possible. We describe the required optimization as a seed-selection problem in the context of firestorms by explaining the differences it has compared to its examination in other existing contexts. We propose a new seed-selection method that is based on the concept of local centrality, which unlike existing social network analytics, selects supporters based not on the global structure of the social network, but locally, i.e., by taking into account the areas of a social network that have been affected by the negative word-of-mouth. Experimental evaluation with data from a real social network demonstrates that the proposed method presents several advantages compared to seed-selection based on commonly used global centrality scores.

Keywords: Online Firestorms, Social Media Phenomena, Social Network Analytics, Network Centrality, Information Diffusion.

1 Introduction

Social media have become an important part of the everyday life of companies, since they offer direct communication channels with their customers. However, they also make companies susceptible to negative word-of-mouth (nWOM) (Hennig-Thurau et al., 2010), that is, comments about an organization’s products, service quality, or trustworthiness, which are passed on from one person to another and may adversely affect its business (Richins, 1984). This can cause the emergence of social-media phenomena, such as online “firestorms”, which are sudden discharges of large quantities of nWOM that spread rapidly in social media (Pfeffer, Zorbach and Carley, 2013). The reasons for the emergence of firestorms can be varying. It can be due to a marketing campaign that backfired, for example the Twitter campaigns of McDonald’s, which asked people to share their stories using a

Mochalova and Nanopoulos /Restricting the spread of firestorms in social networks


specific hashtag. The campaign backfired when people started sharing negative stories. Another reason can be the dissatisfaction of customers and public with the company or its products; for instance, the insurance company Progressive faced an online firestorm after defending an offender in order not to pay out victim’s insurance policy.1

The affective and viral nature of firestorms poses severe threats with potentially unforeseen and uncontrollable consequences, such as harming brand reputation and causing customer losses (Hennig-Thurau et al., 2010; Pfeffer, Zorbach and Carley, 2013). This motivates companies to monitor social media for nWOM, by using text mining and sentiment analytics (Pang and Lee, 2008), which are becoming available also as online services (e.g. www.NielsenBuzzmetrics.com). Based on this information, companies can create contingency plans and develop forms of counteractions that can be used in case of firestorms. Counteractions can involve proactive or reactive strategies (Van Noort and Willemsen, 2012), where a major role is given to the defense through loyal customers (supporters) who can be engaged into the propagation of positive WOM (pWOM) and, thus, increase resilience to nWOM (Bhattacharya and Sen, 2004). Supporters can spread pWOM in order to destabilize as many people as possible in their negative attitude forming (Pfeffer, Zorbach and Carley, 2013). The involvement of supporters increases the success of a counteraction to a firestorm, because if pWOM were to come directly from the company, people might be reluctant to accept it, since they may perceive it as advertising. In contrast, pWOM from the supporters can spread more effectively, since users of online social networks are influenced more by their social contacts than by direct communication from companies; that was demonstrated in recent surveys, which showed that: “78% of consumers trust social peer recommendations over traditional web advertising”.2

Motivated by these factors, our paper aims at investigating firestorms and focuses on how social network analysis can be applied to the problem of restricting the spread of nWOM by optimizing the counteraction through the involvement of supporters. The main research question addressed is how to identify the appropriate supporters (called seeds) that will initiate the propagation of pWOM that will constrain the spread of the nWOM as much as possible. Our approach focuses on optimizing counteractions to firestorms, where pWOM is used only as a mean of minimizing the spread of nWOM. Maximizing the spread of pWOM is not identical to minimizing the spread of nWOM, because minimization of the number of negatively activated nodes can be performed through few but well selected seeds, which will prevent many other nodes from becoming negatively activated even by staying inactive, i.e., not necessarily becoming positively activated. In contrast, the positive activation of several nodes may not necessarily be able to prevent many other nodes from becoming negatively activated, because those positively activated nodes might not had been exposed at all to nWOM and thus they do not correspond to prevented negative activations.

In this paper we investigate how seed-selection methods based on centrality can be used to constrain the spread of nWOM. We propose a novel method that, unlike existing seed-selection methods based on global centrality (i.e., how central is a member in terms of the entire structure of a social network), selects seeds according to their local centrality, which is defined in terms of both the structure of the social network and the members that have been already affected by nWOM. The experimental results show that our method compares favorably to seed-selection based on global centrality.

The rest of this paper is organized as follows: in Section 2 we present the related work and explain in more detail the motivation for this study. In Section 3 the examined problem and the proposed

1 For both cases see more details at: www.rawstory.com/rs/2012/08/16/online-firestorm-erupts-after-progressive-defends-womans-killer/ and intentious.com/2011/11/23/qantasluxury-crashes-into-ground-we-take-twitter-down-for-the-ride/ 2See www.effectwebagency.com/resources/3-Major-Risks-of-Casually-Investing-in-the-Web-white-paper.pdf



methodology is described. In Section 4 the structure and setup of our experimental evaluation is presented, with the results being presented in Section 5. Finally, Section 6 concludes the paper.

2 Related Work

Firestorms have only recently started to be investigated as social media phenomena that involve nWOM against a person, company, or group, and create the need for developing effective counteractions (Pfeffer, Zorbach and Carley, 2013). Among the various forms of possible counteractions to nWOM in social media (Hennig-Thurau et al., 2010), the spread of pWOM by supporters has been identified as a very effective mean (Van Noort and Willemsen, 2012), especially in the case of firestorms (Pfeffer, Zorbach and Carley, 2013). Although these existing studies motivate the use of supporters in general, they do not propose specific methods with which seeds can be selected in an optimal way that will constrain the spread of nWOM during a firestorm as much as possible. In this paper, we try to close this gap by proposing a method for this seed-selection problem.

The seed-selection problem in online social networks is mainly a computing one – based on information available about the network, one needs to identify influential users to start the viral spread (Probst, Grosswiele and Pfleger, 2013) and predict how this spread will diffuse in the network (Fang et al., 2013). Seed-selection has been mostly studied in the context of viral marketing, where the main goal is to maximize the number of users that will adopt the message of a viral campaign. This direction of research was pioneered by Kempe, Kleinberg and Tardos (2003), who proposed models of information diffusion that investigate how a specific piece of information propagates in an online social network and activates its members during a viral marketing campaign. A limitation of existing approaches in this research direction is, however, that they require information about influence factors in the network, i.e., the amount at which users influence one another (Goyal, Bonchi and Lakshmanan, 2012). The exact quantification of influence factors requires data that is often not available or cannot be used due to privacy reasons. To overcome this limitation, centrality scores have been used that select as seeds users that have a globally central position within the structure of a social network and, thus, can reach a larger part of the network (Hinz et al., 2011).

Another limitation of all aforementioned approaches is that they are applicable only to the case where a single homogeneous piece of information is being diffused, which in the context of viral marketing can be considered as a form of pWOM. However, they do not take into account the possibility that nWOM may be propagated at the same time. To address this, several extensions to existing models have been proposed that incorporate negative opinions (e.g. Chen et al., 2011, He et al., 2012). This holds, for example, when two companies engage in marketing campaigns competing for customers. But these studies focus mostly on the problem of seed-selection in terms of maximizing the spread of pWOM in the presence of nWOM, by activating as many nodes as possible for one of the campaigns and prevail over competitor (Bharathi, Kempe and Salek, 2007; Carnes at al., 2007; Goyal and Kearns, 2012), but not on constraining the opposite campaign – which is the goal in restricting firestorms.

A limited number of works have focused on minimizing the spread of the competing contagion, which is similar to the goal of this paper. One of such studies (Budak, Agrawal and El Abbadi, 2011) proposed a diffusion model for two types of information spreading simultaneously in a social network, where the first type corresponds to true and the second to false information. Seed-selection methods have been proposed to start the propagation of true information that will limit the spread of false information. Specifically, seed-selection has been performed based on a greedy hill-climbing algorithm, a centrality score, and some heuristics based on prediction of nWOM spread. However, all these methods (apart from the centrality score) require knowledge of influence factors, which can be a limitation as described above. More importantly, the case of true-versus-false information spread



closely resembles the case of defamation, i.e., communication of false statements that harm the reputation of organizations or individuals.3 Based on this, the approach of Budak, Agrawal and El Abbadi (2011) is based on the premise that individuals, when faced with both true and false information, will always accept the true one, because the false information can be easily disproved. This premise, however, does not hold in the context of firestorms, since the decisions of individuals are not only affected by their personal inherent preferences, but also by the so called negativity bias that makes them more likely to accept and propagate nWOM (Rozin and Royzman, 2001).

To summarize, seed-selection has been examined in the context of the following applications:

• Viral Marketing. Only one type of information (pWOM) is being spread and seeds are used to maximize this spread (Kempe, Kleinberg and Tardos, 2003; Hinz et al., 2011).

• Competitive Marketing. Two or more competing messages are being propagated through word-of-mouth. They are represented by multiple cascades, where pWOM and nWOM compete for attention of users in a network (He et al., 2012; Chen et al., 2011; Bharathi, Kempe and Salek, 2007; Carnes at al., 2007; Goyal and Kearns, 2012). The goal of seed-selection is to maximize the spread of pWOM, and not to limit the spread of nWOM.

• Defamation. nWOM in form of false information being propagated competing with pWOM in form of information proven true (Budak, Agrawal and El Abbadi, 2011; Nguyen et al., 2012). When facing both nWOM and pWOM, user will accept the latter as it contains the proof of its verity.

We focus on firestorms where both pWOM and nWOM are being spread in a social network, and nWOM is not representing false information that is self-evidently discarded when contradicted with pWOM. Our approach focuses on the objective of constraining the spread of nWOM as much as possible and our seed-selection method considers a local target in order to constrain firestorms.

3 Proposed Methodology

3.1 Problem Description

A social network represented by a simple, undirected4, and unweighted graph G(V,E) is given. V is the set of nodes corresponding to the users of the network and E is the set of edges corresponding to the social ties among the users. Each node of V can be inactive, negatively activated, or positively activated. Initially, all nodes are inactive and once nWOM starts spreading during a firestorm, nodes exposed to nWOM may become negatively activated. We examine the so called progressive spread of WOM, where activated nodes (negatively or positively) do not modify their opinions (Kempe, Kleinberg and Tardos, 2003). For a node to become activated (negatively or positively) it is not enough just to be exposed to the corresponding WOM, but also to accept it by performing an action, e.g. “Liking”, posting, or sharing.

Let N ⊂ V be the set of users that have been activated negatively at each time step. The problem of limiting the spread of nWOM can be then considered as identifying a set S ⊂ V of k seed nodes who will become positively activated and start propagating pWOM that will activate positively other nodes that are socially connected to them with edges in E. The number of selected seeds k is predefined and represents the cost of the counteraction to a firestorm. The larger k is, the more seeds have to be

3 See: http://en.wikipedia.org/wiki/Defamation 4 Our approach can be easily extended to the case of directed social connections, such as the directed relation between followers and followees in Twitter.



positively activated initially and we assume that this cost is proportional to k (Kempe, Kleinberg and Tardos, 2003).

Our objective is to constrain the effect of the firestorm, i.e., minimize the number of nodes in N that will be activated negatively in the end. Therefore, we do not focus on maximizing the final number of positively activated nodes.

3.2 Selecting Seeds based on Local Centrality

Existing research proposed to select seeds according to how central their position is with respect to the network structure represented by graph G (Hinz et al., 2011). The intuition is that, the more central a node is, the more likely it is to reach many other nodes. By computing a centrality score c(v) for each node v ∈ V, we select the top-k nodes with the highest scores as seeds. In the case of a counteraction to a firestorm, when central nodes are selected as seeds, they are expected to be more effective in spreading pWOM. Moreover, by selecting central nodes as seeds, we prevent them from becoming negatively activated, and thus we prevent negative activation that could have been achieved by them.

Several algorithms have been proposed to compute centrality scores, such as degree, betweenness, closeness and Eigenvector centrality (see Borgatti and Everett (2006) for more details). Initial experimental comparison of some of these centrality scores indicated that they have comparable performance (Hinz et al., 2011), however Eigenvector centrality has been recently reported to have the overall best performance (Goyal, Bonchi and Lakshmanan, 2012; Mochalova and Nanopoulos, 2012). That is why in this study we focus on Eigenvector centrality – it is defined as the principal eigenvector of the adjacency matrix defining the network. It computes relative scores to all nodes in the network based on the principle that connections to nodes having a high score contribute more to the score of the node in question, i.e., not only the connectedness of each node analyzed but also the connectedness of neighboring nodes is also taken into account. A variant of Eigenvector centrality is, for example, involved in Google’s search engine.

The aforementioned centrality score can be characterized as global, because it is computed based on the entire network structure. Despite their aforementioned advantages, global centrality scores present also the following disadvantages in the case of selecting seeds for a counteraction to a firestorm:

1. Global centrality scores ignore the nodes in set N, which have been already negatively activated. This means that the counteraction to a firestorm tries to initiate the propagation of pWOM, by selecting seeds that have high global centrality, regardless of which nodes have been already affected by nWOM. However, seeds with high global centrality may be far away, in terms of the topology of the network structure, from the negatively activated nodes in N. Thus, they may not become able to prevent many negative activations (despite the fact that they may achieve many positive activations – see the discussion in Section 3.1 about these two different objectives). Additionally, recent findings showed that influence propagation in viral processes in social networks often happens only within a close proximity of the seeds (Cha, Mislove and Gummadi, 2009), thus spread started with a globally central seed might not even reach the contaminated area. By using local centrality scores (White and Smyth, 2003), the target (contaminated area) is taken into account, their performance, however, were not yet considered for firestorms.

2. The above problem becomes worse when considering that pWOM initiated by seeds that are globally central requires intermediate nodes to further propagate this pWOM in order to reach the areas of the network that contain the negatively activated nodes. Therefore, selecting seeds based on their global centrality is based on the premise that intermediate nodes will be also willing to perform such further propagation of pWOM. This premise may not be valid in general (Aral, Muchnik and Sundararajan, 2013) – even if intermediate nodes become



positively activated, they may be unwilling to further propagate pWOM to their friends (we examine this issue in more detail in our experimental study in Sections 4 and 5).

3. It is assumed that nodes with high global centrality scores are always available to become seeds. Nevertheless, global centrality represents a measure of node importance in a social network and, thus, it may be harder to convince nodes of pronounced importance that have high global centrality to become seeds that will spread pWOM (Hinz et al., 2011). More importantly, due to the first disadvantage above, global centrality scores remain unchanged as long as the network structure is not changed. This means that the same top-k nodes with the highest global centrality scores have to be always selected, assuming again that they will be always willing to engage with every counteraction to several different firestorms, because each one will try to activate them as seeds for the propagation of pWOM. Evidently, this naïve assumption does not reflect reality.

To overcome these disadvantages, we developed a local centrality score, which takes into account the already negatively activated nodes in N. The proposed score examines the neighbors of nodes in N (i.e., nodes that are connected to nodes in N with edges from the set E defined in Section 3.1) and selects as seeds among them those neighbors with the highest Eigenvector centrality score. (We focus on Eigenvector centrality because of its good overall performance as mentioned above; however other centrality scores can be used, too.) An example is depicted in Figure 1. The checkered node represents the node that initiated the propagation nWOM. This node managed to negatively activate its neighbors, which are depicted as black colored. The local centrality score will consider all neighbors of these negatively activated nodes; these considered nodes are depicted as hatched. Among those, the top-k with the highest Eigenvector centrality will be selected as seeds.

Figure 1. Example for the local centrality: the checkered node is the initiator of a firestorm;

Black nodes are negatively activated; Hatched nodes will be considered as seeds of the counteraction; White nodes are not activated yet.

The local centrally score avoids the first disadvantage of global centrality because it takes into account the set of negatively activated nodes N, by considering as seeds only nodes that are neighbors of nodes in N. It avoids also the second disadvantage, because seeds with high local centrality are closer to the area of the network that is affected by nWOM, and thus they can become more effective in constraining farther spread of nWOM, because they can positively activate nodes around this area that will “block” the farther spread of nWOM without the need of having many intermediate nodes that are willing to spread pWOM. The local centrality score also avoids the third disadvantage, because it does not necessarily select nodes with high global centrality. Therefore, by being less pronounced, seeds with higher local centrality may be more available for spreading pWOM. Moreover, seeds selected with local centrality will be different for different counteractions, because they will have a different set of negatively activated nodes N, which affects the computation of local centrality scores.



3.3 The Examined Diffusion Model

To be able to test the performance of the proposed local centrality score (see Section 3.2), we implemented diffusion processes over the structure of a given social network (the details for the real data set that we used will be given in Section 4.1). For this purpose, we focused on a widely applied diffusion model that is called Independent Cascade (IC) (Kempe, Kleinberg and Tardos, 2003). Given the structure of a social network, which as described in Section 3.1 is represented by a graph G(V,E), IC starts by activating the seeds and then continues in discrete steps. When a node v becomes active at time step t, it has a single chance to activate each of the currently inactive neighboring nodes connected to it. For each such neighboring node w, node v has probability pvw to succeed in activating w with the same status as v (positive or negative). If v succeeds, then w becomes active at step t + 1 and recursively tries to activate its own currently inactive neighbors. Otherwise, v makes no further attempts to activate w. The process runs until no more activation is possible.

This model is an extension of the existing IC model (Kempe, Kleinberg and Tardos, 2003). Our extensions include the following: i) incorporation of a stopping probability (described in detail at the end of this Section); and ii) modifying the way the probability pvw is defined, by not just being dependent on the influence one node has on its neighbor, but on the following three factors:

1. Influence factor ivw that represents how much influence node v has on w, i.e., how likely is w to become activated by node v. We computed influence factors based on the intensity of communication between each pair of nodes (see Section 4.1 for more details). Influence factors represent the social influence among members of social networks (Kempe, Kleinberg and Tardos, 2003). 2. Inherent preference θw that user w has about the element (product, brand, etc.) for which nWOM and pWOM are being spread (Aral, Muchnik and Sundararajan, 2013). We assume that θw is a random variable that follows Beta distribution (i.e., θw ~ Beta(α,β)) and takes values in the range [0, 1]. Values closer to 0 (closer to 1) indicate lower (higher) susceptibility to the firestorm. When the value of θw is closer to 0.5, then w has a neutral inherent preference and is equally likely to get convinced by nWOM and pWOM. The factor of inherent preference represents the so called anchoring effect that has been identified to cause individuals to be biased towards their inherent preference (a.k.a. attitude); thus, the stronger their inherent preference, the more resistant they are to changes of external factors such as social influence represented by the influence factor (Ahluwalia, 2000). 3. Negativity bias n, which increases the probability of v activating its neighbor w when v is activated negatively, and decreases that probability when v is positively activated. The factor of negativity bias causes nWOM to have more impact than pWOM (Rozin and Royzman, 2001), since individuals are relatively more likely to be influenced by negative than positive experiences, as have been identified in studies about social media.5 We represent negativity bias through 𝑛, a small (positive) constant.

Although these three factors have been identified in existing research (see citations above), they have not yet been considered in diffusion models like IC. Therefore, although they may not be exclusive (additional factors need possibly to be investigated), their consideration can enhance the IC model.

Based on the above factors, when a node v tries to activate a currently inactive neighboring node w, then the probability of activation depends on the status of v (i.e., whether v is already activated positively or negatively) and is calculated as following:

𝑝𝑣𝑤+ = 𝑖𝑣𝑤 ∗ (1 − 𝜃𝑤) − 𝑛

𝑝𝑣𝑤− = 𝑖𝑣𝑤 ∗ 𝜃𝑤 + 𝑛

5 See: http://www.businessesgrow.com/2012/03/20/we-are-all-standing-on-digital-quicksand/



Unlike the IC model that considers only positive activations and assumes for each pair of nodes a single probability pvw, in our extended IC model we account for the fact that nodes can be activated positively or negatively. For this reason, we consider two probabilities: 1) 𝑝𝑣𝑤+ , i.e., the probability to activate w positively when v is already positively activated; and 2) 𝑝𝑣𝑤− , i.e., the probability to activate w negatively when v is already negatively activated. Therefore, w is more likely to activate (either positively or negatively) as influence factor ivw increases – the more influential node v is the more it affects its currently inactive neighbor w. Moreover, the activation of w is also affected by its inherent preference θw, where θw values closer to 0 (i.e., 1-θw values closer to 1) increase the likelihood of positive activation (the other way around for values closer to 1; see the discussion above). Finally, by adding (subtracting) the constant factor 𝑛 from (to) 𝑝𝑣𝑤+ (𝑝𝑣𝑤− , respectively), negativity bias makes negative activations more likely relatively to positive activations.

We have to emphasize that we consider all aforementioned factors (influence factor, inherent preference, negativity bias) only during the implementation of diffusion processes that reproduce spreads of nWOM and pWOM in order to experimentally test the proposed local centrality score in the way that is described in Section 4. Thus, to compute all centrality scores (local and global) we assume no knowledge of these factors and do not take them into account during the seed-selection, which is based only on the structure of the network. This is in accordance to the discussion in Section 2, because as mentioned there, these factors are latent and not easy to be measured in real applications (sometimes it is also not allowed to measure them in online social networks due to privacy reasons). However, these factors are used to evaluate the performance of centrality scores in our experimental study (Section 4), because they are needed to operate the IC model.

Finally, our extended IC model considers a stopping probability: when a node gets activated positively, it may not necessarily try to activate its neighbors. This reflects the case when user becomes positively activated but is not willing to participate further by propagating pWOM. This is contrast to the standard IC model (Kempe, Kleinberg and Tardos, 2003), which makes the assumption that each node is always willing to further propagate pWOM. The use of a stopping probability is relevant to firestorms because a lot of users may be reluctant to engage in the spread of pWOM, even if they have been positively activated. However, we do not use a stopping probability in case of nWOM because we assume that users that become activated negatively are more eager to propagate nWOM. This is another manifestation of the negativity bias mentioned above, which is based on the psychological arousal that nWOM is able to create (Rozin and Royzman, 2001).

4 Experimental Design

In this section, we describe the design of our experimental study that compares the centrality scores presented in Section 3.

4.1 Data Set

For the experimental study we use a real data set about Facebook users from New Orleans regional network that has been made publically available by the Social Computing Group at Max Plank Institute6. The data set contains 60,290 nodes connected by 1,545,686 edges in the social network. The average node degree is 25.3. The data contains the information about interactions between nodes. These interactions are represented by “wall posts”, a broadcast-style messaging between users on Facebook. The data set contains 838,092 “wall posts” which average to 13.9 “wall posts” per user. For

6 The data set is available at: http://socialnetworks.mpi-sws.org/



the tasks of seed selection based on centrality scores, an undirected and unweighted graph representing the structure of this network was constructed.

In order to test the performance of proposed methods using the diffusion model described in Section 3.3, a corresponding directed and weighted graph was built. This graph contains influence factors and is used only to measure the performance of each seed selection method and not for selecting the seeds themselves, which are selected based on the undirected and unweighted graph mentioned above. To build the weighted graph, information about the “wall posts” was used. Following the approach commonly used in related research (Kempe, Kleinberg and Tardos, 2003), we assume that the number of “wall posts” that user v sends to user w is an indicator of the influence that v has on w. The influence factor that v has on w is then normalized by dividing the number of messages sent from v to w by the total number of messages sent to w. This way, all influence factors are in the range between 0 and 1, and the total sum of influence factors on each node is equal to 1. The weighted graph with influence factors ivw is used to calculate the probability of activation in IC model during the experimental evaluation (see Section 3.3. for more details).

4.2 Performance Measure and Model Parameters

The success in constraining the spread of nWOM is measured with the number of prevented negative activations (PNA), which is the total number of nodes that

• are not activated negatively when a counteraction has been performed; • but would had otherwise been activated negatively if a counteraction had not been performed.

The latter condition is tested by running the same diffusion process (based on the model presented in Section 3.3.) with and without the use of a seed that implements the counteraction by propagating pWOM. To simplify the presentation, we present PNA as a percentage of the total number of nodes that are activated negatively if counter-campaign does not take place. Thus, a PNA value of x% means that the counteraction managed to “save” x% of the negative activations that would have happened. Evidently, higher values of PNA correspond to a more successful counteraction.

The examined values of the parameters of this model are set as follows:

Inherent preference of users in the network follows Beta-distribution Beta(α,β) with α = 2 and β = 2. This corresponds to the most natural case of preference distribution in social networks, where most users are quite neutral to the propagated piece of information but there are some users with rather positive attitude and some with rather negative attitude. When assigning inherent preferences to users, we take into account the homophily principle, which states that individuals tend to socially relate to others with similar tastes and preferences. As a consequence, individual preferences correlate between people connected by social ties (Peres, Muller and Mahajan, 2010). In our case, we assume that users connected to each other will have similar inherent preferences, for example, negative, positive, or rather neutral. However, we do not implement a pure homophily structure, but we instead assume that with some probability (in our case 30%) a neighbor of the user will have different or opposite inherent preference. This is used because in reality pure homophily is expected to be rare.

Negative seed set size is set to be 1% of the total number of nodes. Negative seeds are the nodes that initiate the spread of nWOM by the firestorm. They are selected randomly among the top 3% of the most central nodes (according to Eigenvector centrality). This corresponds to a challenging case, because it allows the firestorm to have a major impact.

Positive seed set size corresponds to the number of nodes that will be positively activated and start the spread of pWOM as counteraction to the firestorm. Naturally, the bigger the seed set size, the more expensive the counter-campaign is for the company (see discussion about this cost in Section 3.1). We examined a range from 0.6% to 5% and the default value was selected to be 2%.



Delay shows how many nodes have to become activated negatively before the positive seed set becomes activated. This delay shows how quick is the reaction to the firestorm, with 0% being the immediate reaction after the firestorm gets noticed. We examined the range from 0% to 30% of all nodes of the network and the default value is set to 1%.

Stopping probability is used to model the behavior of nodes that are positively activated but do not always try to activate their neighbors (see Section 3.3). When stopping probability is equal to x%, it means that x% of the positively activated users do not try to activate their neighbors. We examined the range from 0% to 95% and the default value is set to be 50%.

Exclusion is used to exclude some percentage of top central nodes from being included in the positive seed. This is done because the nodes with highest centrality scores (the most important/pronounces users of the network) are often difficult and expensive to activate, as was described in the case of the third disadvantage of global centrality scores in Section 3.2. Therefore, through this kind of exclusion, we wanted to see how global and local (proposed) centrality scores are affected when they are faced with the challenge of not having available the involvement of the nodes with highest centrality. When exclusion is equal to x%, it means that x% of the nodes with highest Eigenvector centrality cannot be used in the positive seed set. We examined the range from 0% to 20% and the default is set to 1%. (We have to note that the Eigenvector centrality scores are distributed in a rather skewed manner and the top 1% contains the vast majority of the important nodes.)

Negativity bias is set to 0.01 which brings a small shift of the network towards negativity, without eliminating the chances of pWOM being diffused in the network.

The decision to use these values for parameters was made after a careful and thorough examination of results. The selected values correspond to meaningful cases where there is a possibility of firestorms to emerge (i.e., nWOM can be effectively spread) and pWOM can also become effective in activating nodes. Outside of the selected parameter ranges it becomes either unrealistically difficult or easy for propagation (positive or/and negative) to occur.

5 Results

In this section we compare the performance of global Eigenvector centrality score against its local counterpart proposed in Section 3.2. Each series of experiments takes one of the parameters and varies it whilst other parameters remain default. Since the diffusion processes with the extended IC model have a probabilistic element, each experiment is repeated 10,000 times and the average PNA values are reported. Overall in all of the experiments, local centrality outperforms global one.

In the first series of experiments the impact of positive seed set size is examined. Seed set size varies from 0.6% to 5% of the total number of users in the network. The results of the experiment are presented in Figure 2(a). They show that with small seed set size of 0.6% both scores show similar results by preventing about 7% of negative activations. When the size of the seed set increases, PNA also increases; however, this increase is more pronounced in case of local centrality relatively to the global centrality score. At the same time we are witnessing diminishing return, i.e., the increase in seed set size does not lead to the same increase in PNA, which means that counteractions that involve very large seed sets may not be paying off.

In the next series of experiments, we examine the impact of the delay with which the counteraction starts. The results are presented in Figure 2(b) and show that fast response gives much better results for both methods. However, the local centrality score performs better and, thus, can offer a competitive advantage in cases where some delay in the counteraction is unavoidable, e.g. when the firestorm has not been timely monitored.

The third series of experiments examines the impact that stopping probability (Section 4.2) has on the performance of both the global and local centrality scores. The results shown in Figure 2(c)



demonstrate that, as expected, the performance of both scores decreases gradually with increase of the stopping probability. However, even for large values of stopping probability, the proposed local centrality score outperforms the global centrality score, which indicates that it is more suitable even in challenging cases where the vast majority of users in a social network is not willing to engage in the spread of pWOM.

Figure 2. Number of prevented negative activations (PNA) as percentage of all negative

activations vs. different parameters. Results for global centrality are presented with dotted line and local centrality with solid line.

The final series of experiments examines the impact of the exclusion of nodes with top centrality scores from the positive seed set (see Section 4.2). The results are presented in Figure 2(d) and they show that the local centrality score performs better than its global counterpart. More importantly, the difference in their relative PNA values increases with increasing exclusion: for 0% exclusion global centrality saves 23.2% negative activations whilst local centrality saves 25.8%, but for 20% exclusion PNA become 7.7% and 12.6% respectively. Therefore, in the cases where it is not possible to involve almost any central nodes in the counteraction, the local centrality score performs much better than the global centrality score, and as described in Section 3.2 it avoids the disadvantage of being dependant on the availability of the globally central nodes.

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6 Conclusions

We investigated the social-media phenomenon of online firestorms, which are a consequence of the susceptibility to negative word-of-mouth that companies and organizations suffer because of opening their social media channels to the crowds (Hennig-Thurau et al., 2010). We examined the seed-selection problem in the context of firestorms, which asks for a method of finding users in an online social network that will initiate the spread of positive word-of-mouth in order to prevent many other users from becoming affected by the negative word-of-mouth that is being spread during the firestorm.

Our method is based on local centrality, where the seeds are being selected by analyzing the centrality scores not globally, i.e., based on the entire structure of the social network, but locally, i.e., according to their relation to the users that have been already affected by the negative word-of-mouth. Experimental results showed that the proposed approach performs better and more stable in restricting the spread of firestorms. Moreover, they showed that although factors, such as the delay in the reaction to a firestorm or the unwillingness of rest users to spread further pWOM represent crucial challenges, the proposed method achieves relatively better performance as with respect to these challenges.

There are some important managerial implications from our study: First, the proposed method can allow managers to develop more successful counteractions to firestorms, by utilizing social network analytics (in the form of centrality scores) based on information about the structure of a social network. Such information is in general available, and thus the proposed method avoids the use of critical data that may violate the privacy of users (such as data needed to specify influence factors in several existing related works). The use of social network analysis for studying social media phenomena is an emerging topic of interest both in research and practice, and our study follows this direction. Second, the extended model of information diffusion (Section 3.3), which considers many factors related to firestorms, can offer managers insights that can bring business value, by answering questions such as: “What is the impact of users’ inherent preferences?”, “What is the effect of the size of the seed set and up to which point the involvement of more seeds does not pay off?”, or “up to which delay it is not possible any more to perform a counteraction to a firestorm?”. Such questions can be studied by testing several combinations of the parameters of the model, in order to help managers examine in advance several different scenarios towards the preparation of counteractions.

Our work, however, has some limitations. We consider a static network, whereas social networks are dynamic. We plan to extend our study to include dynamic changes that will need updating of centrality scores. Another limitation is that we assume complete identification of negatively affected nodes. Some communications stay private and, additionally, sentiment-analysis tools might fail to recognize several negatively affected nodes. We plan to extend our work, by enabling partial knowledge of negative spread. We also intend to investigate additional methods of measuring local centrality, such Markov centrality and Shortest paths (White and Smyth, 2003). Finally, we will extend the proposed model to include the possibility of a node to change its state (i.e., non-progressive diffusion).

Acknowledgements Work supported by Katholische Universität Eichstätt-Ingolstadt with the PRO FORschung (PROFOR) project “Innovative Campaign Management System for Viral Marketing in Social Networks”.

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