Of devils, angels and brokers: how social network positions affect misperceptions of political influence

ABSTRACT Misperceiving political opponents as more influential and evil than they are has been described as the devil shift. More recently, the opposite phenomenon known as the angel shift has been recognised where political allies are misperceived as more influential and virtuous than they are. However, research on the devil and angel shifts has been hampered by the lack of measures that separate these mechanisms analytically. We analyse the misperception of influence and differentiate between the devil and angel shifts. Furthermore, previous research has failed to take notice of how social network positions contribute to these phenomena. We argue that conceptualising the different roles that brokers play between advocacy coalitions helps explain the occurrence of the devil and angel shifts. Our findings demonstrate that the devil and angel shifts are not dyadic but triadic phenomena between advocacy coalitions and that network factors accentuate both ‘shifts’.


Introduction
Political sectarianism, in which allies perceive opponents as 'others' and where tribalism and ideological positions overlap with identities, afflicts many Western democracies (e.g., Finkel et al., 2020;Goodman, 2021). Political opponents then become perceived and portrayed negatively: they must be seriously mistaken or up to no good for selfish or malicious reasons (Glover, 2012). Less commonly acknowledged is the tendency to overestimate the omnipotence and influence of opponents, sometimes even to the extent of seeing conspiracies where none exist. The combined effect of these two phenomena, seeing opponents as evil and misperceiving their influence, was first coined in the policy sciences as the 'devil shift' by Sabatier et al. (1987). These authors define influence in terms of the power to change the behaviour of others or situations in a direction an actor wants things to change (e.g., changes in floor votes following major lobbying campaigns) (Sabatier et al., 1987, pp. 452-453). If opponents are seen as omnipotent and thought of as evil, this can give rise to a dynamic of mutual suspicion, which lessens the willingness and ability to forge political compromises. In addition, if political actors misperceive the influence of their opponents, it makes it difficult for them to devise proper political strategies. Therefore, identifying the mechanisms behind the devil shift is of both theoretical and practical importance.
Sabatier argued that the misperception of influence and attributing evilness to opponents would be especially likely in situations of high political conflict. This characterisation can apply, for example, to pluralist political systems and the two-party system. However, the original devil shift idea was not limited to pluralist and majoritarian countries, and Sabatier supposed that the phenomenon also occurs in countries like Sweden, which has corporatist and consensual political institutions. Leach and Sabatier (2005) later proposed the 'angel shift', the opposite phenomenon of the devil shift, which describes how people can also exaggerate the power and virtuousness of their allies. While the angel shift may not be as detrimental as the devil shift for political cooperation, it potentially limits the ability of policy actors to correctly estimate the influence and motivations of their political allies which, as in the case of the devil shift, may impede their abilities to evaluate the current state of the policy subsystem and devise political strategies accordingly.
The ideas of the devil and angel shifts fall under the Advocacy Coalition Framework (ACF), one of the most established theoretical approaches in policy process research, with applications spanning the globe (Jenkins-Smith et al., 2017;Sabatier & Jenkins-Smith, 1999). Central to the ACF scholarship is the study of how allies and opponents coordinate their political behaviour in advocacy coalitions based on shared beliefs (Satoh et al., 2021). The devil shift contributes to coalitional polarization and intransigent conflicts over policy issues. This paper empirically examines when and how the devil and angel shifts occur in Finland, Sweden, Germany, and Japan. In doing so, it makes several contributions. First, the study of the devil and angel shifts has been hampered by difficulties in measurement. We propose a novel way to differentiate the attribution of the devil and angel shifts that takes account of whether the attributed influence is overemphasised or not. Furthermore, previous research has overlooked how the social network position of brokerage contributes to the devil and angel shifts. Research on social networks has shown that occupying the position of a broker increases a policy actor's influence because of a related opportunity to mediate communication between unconnected actors (Fernandez & Gould, 1994). ACF scholars have emphasized that brokerage between advocacy coalitions may define policy outcomes when two or more coalitions compete (Ingold & Varone, 2012). Competition between advocacy coalitions can result in a policy stalemate, and in such cases, brokers can potentially help negotiate a compromise. Brokers can be disinterested observers or can lean towards one or the other coalition. Previous research has often used such measures for capturing brokerage relations that do not differentiate between whether brokerage occurs between allies or opponents. This crucial distinction, however, may help explain the devil and angels shifts. In other words, the ACF literature has not noticed that conceptualising the different roles that brokers play among political allies and opponents is needed to explain when the devil and angel shifts occur.
We demonstrate that the devil and angel shifts are not dyadic but triadic phenomena between advocacy coalitions, meaning that network positions accentuate both shifts. As Sabatier et al. (1987) argued, misperceiving or distorting opponents' goals and resources can intensify conflict and create a disproportionate response by rivals. Furthermore, understanding the reasons for misperceptions of political allies' and opponents' influence is of general relevance as the seeds of political conflict are to be found in these phenomena. We find that devil and angel shifts occur in four countries with varying institutional structures. This means that the problem is likely to be present across a wide range of modern democracies, making it worth the attention of policy scholars and practitioners alike.

The devil shift and the angel shift
One way the field of public policy has incorporated notions of 'us' versus 'them' is with the concepts of the devil and the angel shifts under the ACF (Jenkins-Smith et al., 2017;Leach & Sabatier, 2005;Sabatier et al., 1987). The devil shift is defined as the tendency for policy actors (individuals indirectly or directly involved in a policy issue) to exaggerate the maliciousness and power of opponents; likewise, the angel shift refers to the tendency to overestimate the virtuousness and power of allies. The devil and angel shifts theoretically inform the study of the attraction and repulsion of policy actors in rival advocacy coalitions.
The extent of the devil and angel shifts depends partly on the differences or similarities in policy core beliefs, defined as beliefs central to a policy issue area or policy subsystem (see Jenkins-Smith et al., 2017). According to Sabatier et al. (1987, p. 451), the 'distortion of influence is correlated with the distance between one's beliefs and those of one's opponents'. Thus, when political opponents are ideologically divergent, their influence is exaggerated, and their motives seem unreasonable. Sabatier and his colleagues (1987, p. 453) offered several reasons for exaggerating opponents' influence. Notably, policy actors remember losses to their political opponents more than their own victories (Kahneman & Tversky, 1979). In addition, exaggerating the opponents' power may serve tactical purposes of interest groups trying to promote internal cohesion. Sabatier et al. (1987) also considered that group-think could lead one to overestimate one's power rather than the influence of opponents; however, they thought that the theoretical reasons supporting the devil shift idea were stronger than those suggesting that misperception of influence would be related with one's power.
Empirical studies have explored the devil and angel shifts from varied theoretical perspectives. Leach and Sabatier (2005) linked the absence of the devil shift to trust in collaborative settings. Weible et al. (2011) found a decrease in the devil shift but not an increase in the angel shift in collaborative compared to adversarial governance. Fischer and Sciarini (2015) found no significant effects for the devil shift or the angel shift, and they suggested that the effects of each might cancel each other out.
A lack of agreement on measuring the devil and the angel shifts has hampered research on the phenomena. In particular, operationalising the notion of exaggeration or overestimation has posed barriers for all empirical studies. We propose to measure the devil and the angel shifts in two phases. First, we measure the overestimation of the policy actors' contacts. Second, we differentiate whether this attribution occurs between allies (i.e., 'angels') or opponents ('devils'). In addition, our main theoretical argument is that previous research has overlooked how structural positions can affect the devil and angel shifts. Adding this insight is essential as it connects the 'shifts' with brokerage.

Bringing brokerage into the devil and angel shifts
We incorporate ideas about structural positions into arguments about the devil and angel shifts with the theoretical concept of brokerage. Actors who connect different subgroups of networks can play a critical role in public policy development. For example, Ingold and Varone (2012) argued that in situations of political stalemate, policy brokers help find a compromise between the conflicting aims of advocacy coalitions. Similarly, this argument parallels how policy entrepreneurs connect different streams in the policy process (Herweg et al., 2017) and how brokers connect different social movement sectors (Diani, 2003). In more abstract terms, brokerage is a relation in which one actor mediates two other actors who are not directly linked (Fernandez & Gould, 1994, p. 1457. Policy actors that broker between unconnected pairs of actors gain leverage by enabling the flow of information between a diverse set of actors in a policy subsystem (Fernandez & Gould, 1994, p. 1460. While previous ACF and public policy scholarship has noted the importance of brokerage for overcoming stalemates, we argue that different types of brokerage have relevance for the devil and angel shifts. Brokerage is intimately connected with the devil and the angel shifts because brokerage positions can make policy actors influential in the policy process (Fernandez & Gould, 1994). In addition, when brokerage crosses boundaries between groups, the group affiliation of the broker becomes relevant. More specifically, the brokerage positions between advocacy coalitions can affect the overestimation of the influence of opponents, as in the devil shift, and the inflation of the influence of allies, as in the angel shift. Neither the devil nor the angel shift thus happens on its own but is accentuated by network factors.
In their research on national health policy networks, Fernandez and Gould (1994) found a strong association between the perceived influence of policy actors and brokerage positions. Thus, brokers were likely seen as more influential than other actors (see also Ingold & Varone, 2012). Brokers are actors who most often mediate between the ties that other actors have with each other. However, it is problematic if brokerage relations are treated uniformly. As Gould and Fernandez (1989) argued, the classical literature on brokerage distinguished between different types of brokerage relations and showed that each type of broker plays a different role. Gould and Fernandez (1989) differentiated between five roles that brokers play in triadic configurations where a third actor connects two unconnected actors.
The first role or type is the liaison, in which case all three actors are members of different groups. The second is the local broker or the coordinator who coordinates contact between two actors and where all three actors belong to the same group. The third type is the cosmopolitan or itinerant broker, an outsider who connects two actors belonging to the same subgroup. In the fourth type, the gatekeeper, the broker mediates the connections of a group it belongs to with an outsider. The last type is the representative who is similar to the gatekeeper but with the difference that a fellow group member is connected with an outsider via the broker. Fernandez and Gould (1994) argued that brokers are influential because they exert power in communication networks by connecting unconnected actors. However, they also showed that not all brokerage types are equally important: the coordinator and itinerant types of brokers were more influential than others, although all brokerage positions are positively associated with influence. In addition, there is the caveat that if government actors took a stand on the issues involved, they did not derive influence from liaison and iterant brokerage. The authors, therefore, concluded that governmental actors are not credible as brokers unless they are impartial coordinators.
We incorporate Gould and Fernandez's (1989) brokerage analysis into the devil shift and angel shift concept. While the original brokerage typology was created based on whether a broker connects actors with similar or different issues, our brokerage typology differentiates how a broker connects allies who share policy beliefs, or opponents whose policy beliefs differ. In the context of our research, the groups brokered by the broker are advocacy coalitions where allies are defined by sharing policy beliefs. Consequently, we have four different types of brokerage: representative, gatekeeper, itinerant broker and coordinator. The liaison does not come up in our analysis due to our modification of the original conception (Gould & Fernandez, 1989): the 'heterophilous' ties between actors A-B and B-C already imply that actor A and C share the same policy position, which is the same to the itinerant broker. This is because we treat group affiliation as binary: actors are either allies or opponents with each other. By contrast, in the original formulation by Gould and Fernandez (1989), there are multiple issues with which each actor can engage.
In what follows, we use the term 'ego' to refer to any actor that is the current focus of attention and 'alter' to those actors that ego has ties with. We count the number of times the alter (j) stands in a brokerage position from the perspective of the ego (i). To test for the effect of brokerage relations on the devil and angel shifts, we need to set an adequate contrasting scenario. Other than the case of j being broker, the following configurations are also possible: (1) there is no tie between i and j, (2) i is at a brokerage position, and (3) i, j and k are in a triadic closure (i.e., all are connected with each other). In addition to these configurations, the dyadic configuration between i and j (i-j is connected and neither i-k nor j-k are connected) is also theoretically possible. However, this is the case only when i and j are connected as an isolated dyad that lacks connections to other actors and these instances are rare. Therefore, this configuration was omitted. By definition, the devil shift is only possible between an ego and an alter whose policy beliefs are different from each other because it is a thesis about how opponents are seen, whereas the angel shift occurs between allies that share beliefs. Figure 1. lists the possible configurations related to the angel and devil shifts. In the first one, ego i and alter j are not connected. Second, i instead of j stands in a broker position. Third, j is not a broker because both i and j are connected with a third actor k(s) (labelled 'embedded'). The subtypes are further depicted based on each actor's beliefs in Figure 1. The configurations other than brokerage are the contrast scenarios that enable examination of the alter's brokerage effect. Figure 1 lists the possible brokerage positions in triads of actors. We depict the brokers as either allies ('white') or opponents ('black'), which echoes arguments that many policy brokers can have 'policy bents'; i.e., their beliefs often lean more toward members of one coalition than another (Sabatier & Jenkins-Smith, 1993, p. 27). Some studies have associated brokerage with moderate beliefs (e.g., Ingold & Varone, 2012), but this is not necessary always the case.
Looking at our data, the average actor i tends to be predominantly connected to its opponents (k) through those actors in brokerage positions (j) who hold beliefs similar to i's own, rather than those who hold different beliefs. In addition, wee see no clear evidence that brokerage tends to occur via actors holding neutral beliefs (see Appendix A for details). Moreover, it is useful to differentiate conceptually between an actor holding a brokerage position in the network structure and that actor using its position to engage in brokerage activity. Holding a brokerage position is a necessary condition for brokerage to occur, but whether it actually does depends on many additional factors, such as the choices that actors make and the broader policy context they operate in Ingold and Varone (2012). What we argue here is that holding a brokerage position is what influences an actors' perception about who are the 'devils' and 'angels,' as we discuss in the next section in detail.

Theoretical expectations
From Figure 1 and the theory underlying the devil and angel shift, we derive two hypotheses. First, we expect that the devil and angel shifts do not occur with someone with whom the ego does not know well but with those that ego is connected with. Members of a policy subsystem usually have some knowledge about other members and thus know who is influential based on general information shared among subsystem members. However, we expect that overestimating someone's influence is more likely if an actor has additional evidence of the conduct and views of a policy actor. One source of evidence is being connected to this actor. Thus, we hypothesise the following: H1: Devil-Angel Shift Connection Hypothesis: Actors are more likely to overestimate the influence of those opponents and allies to which they are connected.
Second, as explained above, we expect the extent to which an actor experiences the devil or angel shifts to depend on the positions they occupy in the network (see Figure 1). We posit two hypotheses related to brokerage positions. We expect that the gatekeeper role is associated with the devil shift because, in the gatekeeper role, the ego is connected with a broker who is an opponent with links to other opponents. The fact that the broker is connected with other opponents makes it a likely member of an opposing advocacy coalition. The ego has likely noticed that the alter represents opponents by, for example, acting as a united front with other opponents in political battles. The opposing view has perhaps won some of these previous battles and, as the ACF argues, losses are better remembered than gains, which makes the ego see the alter as influential. Thus, we posit the following hypothesis: In addition, we expect the coordinator role to be associated with the angel shift because, in this configuration, the ego knows that the alter likely belongs to the same advocacy coalition as ego. At the same time, the alter is connected to other allies to whom the ego is not personally connected, perhaps due to a lack of resources. In this case, the alter is seen as influential because it can maintain ties with other allies and is thus well connected, thus suggesting the following hypothesis: H2b: Angel Shift Brokerage Hypothesis: Allies occupying coordinator positionsthose allies that collaborate with other allies to whom the ego is not personally connectedtend to be perceived as more influential than they really are.
We do not expect the other two types of brokerage positions to be associated with the devil shift or the angel shift for the following reasons. In the case of the itinerant type, the brokering alter is not connected with members of an opposing coalition and therefore the devil shift is unlikely. In the case of the representative broker, the alter is not linked with the same coalition as the ego, and the angel shift should therefore not take place. Thus, only two types of brokerage rolesthe gatekeepers and coordinatorsare expected to have an effect on the shifts.

Data
Our empirical data consist of surveys collected in Finland (2014), Sweden (2015), Germany (2012) and Japan (2012)(2013). Finland and Sweden are both corporatist countries where tripartite negotiations between employers and employees are traditionally brokered by representatives of the state. Previous research has found that Sweden may be more consensual than Finland (Gronow et al., 2020), but both countries are in general more consensual than Germany and Japan. The degree of consensus in the latter two countries is regarded to be almost at the same level in terms of the executive-party system, but Germany is more consensual than in Japan in terms of the federal-unitary dimension (Lijphart, 2012).
The data represent the climate change policy subsystems of these countries and were collected as part of the research project COMPON (Comparing Climate Change Policy Networks, see compon.org). The respondents were the most important organizations involved in the domestic climate policymaking process in these countries, and we sampled individuals from these organizations. In most cases, the respondents were either responsible for climate policy or environmental policy in their organisations. The respondents are thus individuals who represent their respective organizations, and we asked them to respond on behalf of their organizationthat is, to think of their organization's positions and collaboration relationships when responding. In the case of most advocacy organizations, however, it is not likely that individual beliefs, collaboration relationships or perceptions of influence of other organizations in the policy domain would differ from organizational ones to a large extent. For example, for an environmental NGO engaged in climate policy advocacy, there is a strong likelihood that the organization employs individuals espousing beliefs that mostly correspond to the organization's mission and policy positions, and conversely, the organizational positions are formulated through a process of aggregation of individual beliefs within the organization. A potential limitation is that while this assumption is likely to hold for most organizations in our sample, it does less well in the case of some others, perhaps particularly universities. Unlike advocacy organizations that usually try to take a clear and unified position on a policy issue they deal with, universities encourage open debate between diverging viewpoints within their organization. However, as universities constitute a small proportion of our sample we do not consider this a serious limitation. Furthermore, we follow common ACF research guidelines in which organizational beliefs and relationships are studied by asking individuals (e.g., Gronow et al., 2020;Ingold & Varone, 2012;Weible et al., 2011).
One question rarely addressed by research on the devil and angel shifts specifically is why one should assume that the psychological mechanisms of overestimating the influence of opponents and allies would apply at the organizational and not just at individual level. We argue that this assumption is reasonable. Even though the mechanisms of the devil and angel shifts concern individual perceptions of reality, in politics people tend to perceive other individuals as members and representatives of groupsthus, seeing the world in terms of us versus them (Klein, 2020). Therefore, we argue that demonizing opponents is based on their perceived group membership. Thus, an opponent is seen as evil and powerful not due to the individual qualities of the person but because of the group that the opponent is taken to represent. Members of environmental organizations, for example, may see individuals representing fossil fuel industries as powerful and evil not because they are bad people per se, but because they work for a fossil fuel lobby organization. We see no reason to assume that similar mechanisms would not work also for the angel shift; thus, allies are allies due to their group membership. For this reason, asking individuals in a survey to think of others in terms of their organizational positions is an appropriate strategy for studying the devil and angel shifts.
While drawing the policy subsystem boundarywho belongs to which climate policy subsystemsit was made sure that the respondent organisations represented different sectors of society (NGO's, business, government, etc.). National experts on climate change helped compile the final list of respondents. Of 99 organisations, 69 actors answered the survey in Sweden (70% response rate), 82 out of 96 organisations answered the survey in Finland (85%), 51 out of 72 organisations answered the survey in Germany (71%) and 72 out of 125 organisations answered the survey in Japan (58%).

Measurement of dependent variables
We operationalise two sides of the original devil shift idea simultaneously: (1) alters are either allies or opponents, and (2) actors perceive alters to be more powerful than they are in reality (i.e., the overestimation of influence).
We define those pair of actors that have similar policy core beliefs as allies and those pairs with different core beliefs as opponents. The ACF distinguishes three different kinds of beliefs: deep core (fundamental beliefs), policy core (basic beliefs but specific to a policy subsystem) and secondary aspects (beliefs concerning particular and technical issues of a policy) (Jenkins-Smith et al., 2017). Policy core beliefs are argued to be the main driver of actors' behaviour in a policy subsystem. We used eight items to construct a composite variable for policy core beliefs. The questions were asked on a five-point Likert scale ranging from 1 (strongly disagree) to 5 (strongly agree). The questions dealt with, for example, the validity of climate science and the necessity to reduce greenhouse gases and capture the most important issues that divide policy actors concerning climate change mitigation. The questions should thus represent policy core beliefs in the climate policy subsystem. Cronbach's alpha for the composite variable was high overall (a = 0.86) and also for each country (0.87 in Germany, 0.84 in Finland, 0.87 in Japan and 0.82 in Sweden). Accordingly, we created a composite variable or the policy core belief score using principal component analysis. To make the variance of the scores similar across the countries, the original score was standardised in each country before submitting it to the principal component analysis.
The respondents' perception of the influence of other actors on policy was derived from the question 'Which actors are especially influential for domestic policymaking?' Conceptually, the answer contains both estimations of 'real' and overestimated influence. We differentiated between real and overestimation of influence based on the overall assessment of an actor's influence. If a respondent indicated an organizationl actor as being influential and other respondents also thought so, we treat the respondent's assessment as 'real'; if a respondent thinks an actor is influential but other respondents do not agree, we treat this assessment as an overestimation of influence. Studies show that the measure we use to assess real influence, i.e., the aggregate estimation of an actor's influence by other actors in the same policy subsystem (also called reputational power), is a very good proxy for actual influence. In other words, the other actors in the policy subsystem, in the aggregate, can estimate how influential each actor is, despite the perceptions of some individual actors being distorted by the devil and angel shifts (Fischer & Sciarini, 2015). Concretely, the respondents were presented with a roster of organizations and asked to check those whom they perceive as influential, and this roster was identical to the list of respondents. We also asked respondents to add any organizational actors they thought were missing from the roster, but this proved to be rare, which we take as evidence that the main actors of the climate policy subsystem in each country were listed in the rosters. The answer was summarised in a matrix format in which entry one represents that the actor in row (i) (i.e., the respondents) considers actor in the column (j) influential, and 0 otherwise. 1 We name this original matrix the raw influence matrix. Next, using the sum of the entries in each column of the raw influence matrix (i.e., the information about the aggregate assessment of each actor's influence), we created a hypothetical influence matrix to represent a situation in which all respondents would have given the same answers to the question of which actors are influential; hence, there is no overestimation in this hypothetical matrix. We then compared the raw influence matrices with the hypothetical influence matrices. Through this comparison, we identified which entries in the raw influence matrix is 'abnormal' in the sense that a respondent identifies an actor as influential even though the actor is not influential according to the aggregate assessment of the other respondents.
Once we identified cases of overestimation of influence, we differentiated them in terms of whether they are between allies or opponents by referring to the policy core belief score of i and j. The entry in the devil shift matrix is 1 if i overestimates j's influence and they are opponents and 0 otherwise. Likewise, the entry in the angel shift matrix is 1, when overestimation occurs between allies. Those alters whose policy beliefs differ by more than one standard deviation from the ego are regarded as opponents, otherwise as allies. Appendix B provides a detailed illustration of how this works. Note that we also performed the same differentiation of entries between allies and opponents in the raw influence matrix when analysing it.

Measurement of independent variables
The data on collaboration were collected in the same manner. The respondents were asked to indicate all organisations they 'collaborate with on a regular basis'. The original collaboration network is binary and directed, but it was transformed into a symmetrised network, which means that we regard collaboration to exist between i and j not only when both agree but also when either of them thinks this to be the case. This data transformation helps to operationalise the brokerage typology without too much complexity.
Our main independent variable is each type of triadic configuration in the collaboration network (see Figure 1). We counted the number of times the alter stands as brokerage position in the triplet (i.e., in the triplet of {i, j, k 1 }, {i, j, k 2 } … {i, j, k n−2 }). The count of each triadic configuration is log-transformed (the original count plus 1 so that 0 indicates no relationship). Whether an alter j and the third actor(s) k are an ally or an opponent to the ego is determined by their policy core beliefs (see Section 5.2.1). We focus on the egos' perspective towards the alters. Accordingly, we are interested in the number of times j stands at the brokerage position in the triplet comprising i, j and a third actor, k.

Control variables
We explore several competing and complementary explanations against our two main hypotheses. Although these factors have theoretical importance, we treat them as control variables (CV1-CV7) given that the main theoretical focus of the paper is on the structural factors driving the devil and angel shifts.
. CV1, Governmental actors. Governmental actors are likely to differ from other organisation types (i.e., political parties, scientific organisations, business actors, and NGOs) because they are, at least in principle, less likely to question the legitimacy of actors holding beliefs different from their own (Sabatier et al., 1987, p. 449). Governmental actors are also hypothesized to have more moderate policy beliefs than interest groups (Jenkins-Smith et al., 2017, p. 148), and, therefore, they will be relatively close to any opponent or ally. Thus, we control for the possibility that government agencies are less likely to overestimate the influence of their opponents and allies than other actor types. To control this effect, each type of actor is coded with the dummy variables. The type of sender (i.e., the effect on the actor itself) and receiver (i.e., the effect on actor's contacts) are differentiated. . CV2, Organisation type similarity. Similar kinds of actors acknowledge each other's power more often than the power of actors that are of a different type (Fischer & Sciarini, 2015;Knoke, 1998;Leach & Sabatier, 2005;Weible et al., 2011). Moreover, actors of the same organisational affiliation will more likely have similar beliefs. There will likely be less belief difference among actors of the same organisational type and an increase in the likelihood of belief differences between actors of different organisational types. Thus, we control for the possibility that actors of the same organisation type are less likely to overestimate their opponents' influence (devil shift) and more likely to overestimate their allies' influence (angel shift). We included a dummy variable matrix in which 1 indicates actor type similarity and 0 otherwise. . CV3, Influential neighbourhood effect. Actors may project the properties of an actor's network partners onto the actor. In the case of influence, this would mean that actors located in influential neighbourhoods within a network would be perceived as more influential than they are. We control for the possibility that policy actors are more likely to overestimate the influence of those who collaborate with many influential actors (devil and angel shifts). This was measured by the sum of the influence score (i.e., the number of times and actor was named influential by others) of the third actors to whom the alters were connected. Alters who were connected with many influential actors can receive more devil or angel shift ties than those that are not (receiver effect). . CV4, Belief distance. Controlling for belief distance draws directly from the definition of the devil and angel shifts and the notion that perceptions of other actors is conditioned by differences in beliefs about public policy.
We control for the possibility that the greater the belief distance between two actors, the more likely one is to overestimate the other's influence if the other is an opponent (devil shift), and the less likely one is to overestimate the other's influence if the other is an ally (angel shift). This is measured by the absolute difference of the policy core beliefs between the ego and the alter. . CV5, Collaboration partners. Those actors that collaborate with many others are less likely to experience conflict than relatively isolated actors (Heikkila & Weible, 2017). Moreover, actors with many collaborative partners tend to be considered more influential (Fischer & Sciarini, 2015;Heaney, 2014). We, thus, control for the possibility that the more collaboration partners an actor has, the less likely it is that its influence will be overestimated by opponents (devil shift) and the more likely it is that its influence will be overestimated by allies (angel shift). . CV6, Institutional structures. It is also likely that institutional factors affect the emergence and management of policy conflict and, hence, the devil and angel shifts. Consensual political institutions may be more able to manage policy conflict and make the devil shift less likely. The potential association between macro-political structure and the devil shift echoes Weible et al.'s (2011) claim that the more collaborative the context of governance is, the less likely the devil shift becomes. Thus, we control for the possibility that the devil shift phenomenon will be more prevalent in countries with conflictual institutional structures. For the sake of comparability between the models, we also control for the institutional effect for the angel shift even though we do not expect the angel shift to be affected by institutional differences. . CV7, Overall influence attribution. Lastly, the susceptibility to the devil and angel shifts may vary depending on how prone an actor is to name others as influential. For those actors who name many others as influential, the general sense of influence in the network may be inflated, making them prone to the devil and angel shifts. We thus control for the possibility that the more alters an actor names as influential, the more likely this actor will overestimate the influence of their opponents and allies (devil and angel shifts).
To find the factors that cause the devil and the angel shift, we apply a Bayesian cross-classified multilevel logistic model. To use this model, we vectorised the original devil and angel shift matrix, which means that the primary unit of observation is respondents' (i) perception of alters ( j). Because these data are nested under both i and j, we used a cross-classified multilevel model. In other words, we utilised the ego-alter tie analysis of the egocentric network approach (Perry et al., 2018;Vacca et al., 2019). Exponential random graph modelling (ERGM) is common in the context of network analysis but was not applicable in our case. ERGMs find the probability of the existence of a tie against the nonexistence of ties in the whole network. However, in our case, some of the ties cannot exist. For example, ties between i and j that share similar beliefs cannot exist in the devil shift matrix because they share beliefs and, thus, cannot be opponents. Including this non-realisable case as a contrast scenario makes the estimation misleading. In the estimation in our model, we only included cases where ego and alter have different policy beliefs in the estimation of the devil shift effect and similar policy beliefs in the case of the angel shift. When analysing the devil and angel shift, we did not include the cells that were identified as a true evaluation of influence because in these cases the ego correctly identified the alter as influential and no overestimation exists (see Appendix B). Appendix C and D provide descriptive statistics and the results of the principal component analysis of the belief items, respectively. In the following analysis, R (R Core Team, 2019) and R package sna (Butts, 2016), psych (Revelle, 2018) and brms (Bürkner, 2017) are used.

Results
Tables 1 and 2 show the modelling results for the devil and angel shifts, respectively. Our first hypothesis stated that the devil and angel shifts occur more often between connected actors than unconnected ones. Of all unconnected pairs of actors, the devil shift occurs in 8.4% of cases. By contrast, when actors collaborate, it occurs in 17.7% of cases. In other words, the devil shift is more than twice as likely to occur between connected actors as it is between unconnected actors. The angel shift is also more than twice as likely to occur between connected actors (in 7.1% of unconnected pairs of actors versus in 15.3% for connected dyads).
Our devil shift brokerage hypothesis (H2a) stated that opponents occupying gatekeeper positions tend to be perceived as more influential than they really are. The results support this hypothesis. Models 1 and 2 in Table 1 show that the devil shift coefficients for gatekeeper brokers among connected actors are high and statistically significant (.41 in model 1 and .36 in model 2, which includes all controls). This effect becomes even stronger when the alter is connected with many opponents with which the ego does not have a direct tie. The other relationship variables between i-j are statistically insignificant.
The uniqueness of these results becomes more apparent if we compare the devil shift results (model 2) with the raw influence matrix among opponents (model 3). The raw influence matrix of the gatekeeper role has a much smaller effect on influence assessments. Accordingly, the gatekeeper role affects the devil shift phenomenon.  Our angel shift structural hypothesis (H2b) stated that allies occupying coordinator positions tend to be perceived as more influential than they really are. This hypothesis is supported by the results. Among connected actors, the angel shift coefficient is statistically significant at .29 in model 1 and .26 in model 2 (Table 2). This means that allies who are connected with many other allies but with whom the actor is not personally connected tend to be seen as more influential than in reality. Rather unexpectedly, the ego-as-representative configuration also has a statistically significant positive effect on the angel shift (model 2, Table 2). In this configuration, the ego brokers a connection with an opponent and an ally and represents the viewpoint of allies in relation to opponents. The coefficients of the both brokerage types, the coordinator and the ego-as-representative, are larger in the angel shift model (model 2, Table 2) than in influence attribution among allies in general (model 3, Table 2), which means that they relate specifically to the angel shift and the misperception of influence among allies.
For the controls, organisation type (CV1, CV2) seems to have minimal effects on the devil shift (Table 1). Government agencies are equally susceptible to the devil shift as other organisations, and we find no actor type homophily effectactors are just as likely to overestimate the influence of an organisation that is similar to their own as that of any other kind of organisation. Thus, the devil shift does not depend on the attributes of organisations. However, one categorical effect, the influence of NGOs, is less likely to be overestimated by their opponents, perhaps indicating NGOs general lack of influence. For the angel shift (Table 2), we find an actor type homophily effect: businesses, for example, tend to overestimate the influence of their business allies. Actors thus seem to value similar actors to their own. In addition, the influence of scientific organisations and NGOs is less likely to be overestimated by their allies. Thus, the allies of scientific organisations and NGOs seem to have a realistic impression of these actors' influence.
For the devil shift, an influential neighbourhood effect exists (CV3). Being connected with many influential actors makes it more likely that the actor's influence is overestimated by opponents. The belief distance between the ego and the alter (CV4) also makes a difference for devil shift, confirming what previous research has postulated about the devil shift becoming more intense with increasing belief dissimilarity (Sabatier et al., 1987, p. 451). However, both the influential neighbourhood effect and the belief distance effect are also observable in the raw influence attribution model (model 3, Table 1), which contains both normally estimated and overestimated influences. The coefficients in this model for both effects are also higher than in the devil shift model (model 2, Table 1). Thus, it seems that these two effects are related to influential opponents in general and not to the devil shift and the overestimation of influence in particular.
For the angel shift, we find neither the influential neighbourhood effect nor the belief distance effect to be significant (Table 2). Thus, for the angel shift it does not matter whether the alter is connected with other influential actors or if the alter's beliefs are further away from the ego's beliefs; what matters is that people are allies in terms of their beliefs, not the extent of belief similarity.
For both the devil and angel shifts, the number of collaboration ties is significant (CV 5, Tables 1 and 2): those actors with many collaboration ties tend to be viewed as influential by both allies and opponents. This finding contradicts our expectation that actors actively collaborating with others should be less likely to experience the devil shift. However, the coefficient of this effect is much higher in the raw influence matrix (Table 1, model 3). This means that active collaboration does indeed soften the devil shift attribution, partially confirming our expectation of the devil shift. In addition, the effect regarding the angel shift is smaller than the raw influence matrix, which is opposite to our expectation that collaboration would result in additional overestimation of influence.
For the devil shift, the country dummies are significant (CV6) (see Table 1). This finding suggests that there may be some macro institutional effects that affect the devil shift, which are not explained by the brokerage typology. The analysis shows that the devil shift is more prevalent in Sweden and Germany and less prevalent in Japan and Finland (the reference category). Moreover, the angel shift is also more prevalent in Sweden and Germany than in Finland and Japan (Table 2). Actors in two of our case countries are therefore more prone to misperceive the influence of others in general, not that of their opponents or allies in particular. This means that the overestimation of influence does not vary with the countries' institutional characteristics in a way one would expect, as both the devil and the angel shifts are common in countries (Sweden and Germany) that are relatively different from each other.
Finally, we find overall influence attribution (CV7) a statistically significant predictor of both the devil and angel shifts: policy actors who name many others as influential tend to overestimate the influence of both their opponents and allies, compared to those actors who name only a few influential others.

Discussion and conclusion
One of the most perplexing phenomena of political interactions involves the demonisation of opponents, making political compromises difficult or even impossible. Sabatier and colleagues (Leach & Sabatier, 2005;Sabatier et al., 1987) called this tendency the 'devil shift' and its opposite of exaggerating the virtues and power of allies the 'angel shift'.
We presented a novel way to measure the devil and the angel shifts that considers the misperceptions of influence. In addition, we made several interesting findings. First, the devil shift is more common when the alter is a broker in the gatekeeper role. In this case, the alter is an opponent connected with other opponents, which makes the opponent a likely member of an opposing advocacy coalition. Thus, actors who represent opposing advocacy coalitions while being in a brokering position are the ones whose influence tends to get overestimated. We also found two brokerage roles related to the angel shift: actors who were either in the coordinator or the ego-as-representative positions. In the former case, the broker is an ally that connects the ego with other allies. The influence of this allied coordinator is likely to be misperceived because this actor is well connected with other actors. Thus, this is a likely instance of a centrality effect, where the connectedness of an actor is taken to imply status. We did not expect the ego-as-representative brokerage type to be associated with the angel shift but found that it was. In this instance, an actor that brokers connections between an opponent and an ally is seen as more influential than in reality by allies. The fact that the actor represents the viewpoint of the allies in relation to opponents thus makes allies misperceive the influence of this actor.
What do our findings imply for ACF research on the devil and the angel shift? It is commonplace to analyse the misperception of influence without distinguishing whether it takes place among allies or opponents. In addition, previous research has treated the devil and the angel shifts as dyadic phenomena in which two policy actors evaluate each other's influence unconnected from others. Our results suggest that the overestimation of influence is related with brokerage and that different types of brokerage are involved depending on whether the actors in question are friends or foes. Furthermore, by controlling for several other factors besides brokerage, we have been able to provide a detailed analysis of the factors explaining the devil and angel shifts. Previous research has argued that the devil shift would become more intense with increasing belief dissimilarity (Sabatier et al., 1987, p. 451). Our results indicate that opponents are in general seen as more influential when their policy beliefs are very different and this effect is not likely to relate to the misperception of their influence. However, this finding calls for further research.
The original concept of the devil shift contains two ideasactors perceive their opponents to be stronger and more evil than they are in reality. We have concentrated on analysing the first aspect, that of misperceiving the influence of opponents, which is, according to the developers of the concept of the devil shift, the most interesting aspect of the phenomenon (Sabatier et al., 1987, p. 465). The overestimation of influence is easier to address with a survey instrument than the evilness of opponents because we suspect that most respondents would not be willing to label other actors as evil. However, future research might address this issue in a survey by, for example, looking at how other actors perceive the motives of opponents. We suspect that when opponents occupy the brokerage role of a gatekeeper, they are likely to be seen as malicious or evil, as they represent an opposing advocacy coalition. No one has studied whether the opposite of 'evilness' plays a role in the angel shift, which would mean that allies would be seen as good without fault. However, it possible that our results for the coordinator or the ego-as-representative positions in explaining angel shift would also hold when considering the opposite of 'evilness'. Nevertheless, whether there are brokerage positions that make actors seem less evil remains for future studies to determine.
We also found that the devil shift is more prevalent in the Swedish and German than in the Finnish and Japanese climate policy subsystems. This is surprising in the sense that Sweden and Finland are more consensual than Japan and Germany and the literature would lead us to expect that devil shift is more likely to occur in more conflictual settings. Sabatier et al. (1987), after all, argued that the devil shift would be likeliest to occur in contexts of high political conflict, which are common in countries with pluralist and majoritarian institutions. However, they also assumed that the devil shift idea is not limited to such countries and argued that the devil shift would occur in countries like Sweden. Even though we did find some differences among the countries, it is perhaps even more important that we found the devil and the angel shifts to occur across four countries that are quite different from one another in many respects. This shows that the devil and angel shifts likely affect policymaking processes in most modern democracies, and the potential detrimental effects of the devil shift in particular on political trust and mutual understanding are problems to be reckoned with. The association between the devil and angel shifts and specific types of brokerage was present across the four countries we studied. This means that paying more attention to policy brokers can be important not only for scholars but also for practitioners engaged in managing policy processes in ways that build trust and enable overcoming political stalemates.
Our research, thus, helps understand the challenges in our democracies troubled by ideological polarisation, intense policy conflicts and demonisation of opponents (Finkel et al., 2020). These topics have usually been analysed in the context of traditional forms of political engagement, such as voting and elections rather than in relation to interorganizational collaboration in policy processes (exceptions include Goodman, 2021). We have focused on one of the mechanisms that may hamper successful collaboration in tackling complex policy problems like climate changemisperceptions of the influence of policy actorsand shown that actors holding brokerage positions in political networks play a key role in the formation of such misperceptions. Note 1. Influence was asked with a binary questionsomeone either is or is not influentialand this posed some limitations. Actors considered to be very influential tended to get many nominations and it is not possible to tell whether this was an overestimation of their influence or a 'normal' level of reputational power they happen to have. For this reason, we operationalised the overestimation of influence by focusing mainly on the ties among actors who were not extremely influential. This operation should be fine for finding the general mechanism of the devil shift but the downside is that we cannot observe the overestimation of influence among truly powerful actors. Due to this limitation, it remains an empirical question whether our findings on the mechanism of the devil/angel shift also apply to very influential actors. In future research, adding a question where respondents list, say, five most influential actors can help to address this ceiling problem so that the degree of influence attributions can be analysed in a more fine-grained way.