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Chapter 8

Explaining the growth patterns of social movements Peter Hedström

I. Introduction In this paper I focus on the role of generative models in explaining macrolevel dynamics. I argue that most macro-level dynamics of interest to sociologists are sufficiently complex to require the use of generative models, and that the under-formalized nature of sociological theory has hindered our efforts to properly explain many macro-level outcomes. To give substance to the general argument, I develop a model of network-based recruitment to a social movement which shows how the growth pattern of movements are likely to be influenced by the density of the social networks in which they are embedded. During the last few years there has been an increasing recognition that much of what goes under the rubric of sociological theory has little to offer when it comes to explaining concrete social outcomes. The typical sociological “theory” of today is not a theory in the conventional sense of the term i.e., an explanatory tool. Rather, it is an abstract social typology that is meant to provide a “perspective” on society. For most explanatory purposes these typologies are of limited use however, because they normally lack a clear deductive structure that shows how the entities to be explained follow from their alleged causes. Simply postulating that some social event or state X is a cause of Y without specifying the details through which X exerts its influence upon Y can never be an acceptable explanation; the mechanisms providing the detailed link between the cause and the effect must also be specified (see Elster 1989, Hedström and Swedberg 1998, Hedström 2005). The identification of explanatory mechanisms, in particular the reasons for why individuals do what they do, therefore constitutes a core activity in – 111 –

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the construction of explanatory theories; without such micro-level mechanisms the explanations will be wanting. However, although the identification of the relevant micro-level mechanisms is necessary for the development of explanatory theory, it is not always sufficient. In order to explain macro-level outcomes, an additional step typically is required: the mechanisms must be assembled into a generative model which allows us to derive the macrolevel outcomes they are likely to bring about. The paper is organized as follows. First, I briefly discuss the role of mechanisms in explanatory sociological theory. Then I discuss briefly why I believe that generative models are needed for explaining most non-trivial social processes. As noted by Runciman (1998), sociologists tend to spend all together too much time and effort on meta-theoretical discussions like these instead of showing what their theories can actually accomplish. To avoid such meta-theoretical bias, I will try to demonstrate the concrete advantages of the modeling approach advocated here. I focus on the evolution of social movements and on the role of social networks in this process. I focus on this area because it is a substantively important area which is rich on micro-level findings and hypotheses but poor on generative models. I develop a model of network-based recruitment to a social movement and this model reveals results that could not easily have been anticipated without the aid of the formal model. To ensure that the abstract processes being analyzed correspond to real-world social processes, data on the evolution of a Swedish temperance movement is used to calibrate the theoretical model to reality.

II. Mechanisms and explanatory theory The core idea behind the mechanism approach is that we explain social phenomena not by evoking universal laws, or by identifying statistically relevant factors, but by specifying mechanisms that show how the phenomena were brought about (see Hedström 2005 for an in-depth discussion). Philosophers and social scientists have defined the mechanism concept in numerous ways (e.g. Bunge 1997, Elster 1989, Hedström and Swedberg 1998, Glennan 1996, Machamer, Darden and Craver 2000, Pawson 2000), but underlying them all is an emphasis on explaining by detailing how something was brought about; to explicate the cogs and wheels of social processes, to use an apt expression of Elster (1989). A social mechanism, as here defined, refers to a constellation of entities and activities that are organized such that they regularly bring about a particular type of outcome. We explain an observed

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Explaining the growth patterns of social movements

phenomenon by referring to the social mechanism by which such phenomena are regularly brought about. Although the explanatory focus of sociological theory typically is on macro-level entities, an important thrust of the mechanism approach is that actors and actions are the core entities and activities of the explanatory mechanisms. There are at least three important reasons why this is the case. First, it is a well-established scientific practice that theories should be formulated in terms of the processes that are believed to have generated the phenomena being studied. In sociology, this realist principle assigns a unique role to actions because actions are the activities that bring about social change. Second, action-based explanations are, in one particular respect, more intellectually satisfactory than the available alternatives. Focusing on actions and explaining actions in intentional terms provides a deeper and more emphatic understanding of the causal process than do other nonaction-based explanations (e.g. von Wright 1971). Third, action-based explanations tend to reduce the risk of erroneous causal inferences. As noted by Skog (1998), there is considerable risk of mistaking spurious correlations for genuine causal relationships when one focuses on macro-level trends and correlations. One telling example used by Skog is the high correlation often found between sun-spot activity and various social phenomena. The correlation between sun-spot activity and the prevalence of intravenous drug use in Stockholm during the period 1965–70, for example, was as high as 0.91. Action-based explanations can help to eliminate such spurious causal accounts in the following way: if it proves impossible to specify how the phenomenon to be explained could have been generated by the actions of individuals, or if the account must be based on highly implausible assumptions, one’s faith in the proposed causal account is sharply reduced.

III. Generative models and the micro-to-macro link Even if we were exclusively interested in explaining the relationship between two macro-level entities, a proper explanation thus requires us to explicate the micro-level processes that brought about the relationship. Following Coleman (1986) we must first seek to show how macro states at one point in time influence individuals’ action orientations (see arrow 1 in Figure 1); then we must show how these orientations to action are likely to influence how they act (arrow 2), and finally we must show how these actions generate the macro-level outcomes that we seek to explain (arrow 3).

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Figure 1. James Coleman’s Micro-Macro Graph.

As Coleman correctly pointed out, the micro-to-macro relation (arrow 3) has been the main intellectual hurdle for the development of sociological theory. We have reasonably developed tools for analyzing the macro-tomicro relation and for analyzing actions, but when it comes to the microto-macro relation we tend to resort to hand-waving. The reason for this can be sought in the complex nature of the micro-to-macro link. While the other links (1 and 2) can often be analyzed as if they only concerned the actions of a single representative agent, the micro-to-macro link is a dynamic interactive process and it must be analyzed as such because such processes tend to amplify behaviour in complex and often unexpected ways. Under certain conditions, a given event will set in motion a social process that generates considerable macro-level change while under slightly different conditions the same event will generate no change at all (see Schelling 1978 for range of illuminating examples). When actors react individually to an environment that consists mainly of other individuals who are reacting likewise, the macro-level outcomes they are likely to bring about typically cannot be derived without the use of a formal model.

IV. Networks and social movements The example I will use to illustrate the importance of generative models concerns the role of networks in the recruitment of members to social movements. Almost any area of sociology could have been chosen since most of sociology is poor on such models. This area just happens to be one of those that I am most familiar with. A range of studies suggest that social interactions play an important role in the evolution of social movements. Snow, Zurcher, and Olson-Ekeland’s – 114 –

Explaining the growth patterns of social movements

(1980) early and influential study suggested that movement members to a large extent are recruited through pre-existing ties to movement members. McAdam’s (1988) detailed analysis of participants in the 1964 Mississippi Freedom Summer Project confirmed the conclusions of Snow et al. and underscored the importance of social interactions. Sandell’s and Stern’s (1998) study of a local Swedish temperance movement similarly showed that ties to movement members considerably increased the likelihood of individuals’ joining the movement. Sandell (1999) furthermore showed that social interactions are important not only for individuals’ decisions to join social movements, but also for their decisions to leave the movements. His analyses suggested that interactions with previous members of a movement significantly increased the risk that a member would leave the movement (see McAdam and Snow 1997, and Diani and McAdam 2003 for overviews of the most important literature). What these studies suggest is that the propensities of individuals to join and leave social movements are often influenced by interactions with past and current members. As emphasized by Marwell, Oliver, and Prahl’s (1988) it is not always clear why we observe these statistical regularities however. Why should we expect network ties to be of importance in this context? As I have discussed in some detail in Hedström (2005), both belief or information-based mechanisms as well as desire-based mechanisms are likely to be important in contexts such as these. To the extent that there is uncertainty about the benefits to be gained from joining the movement, for example, the fact that friends and acquaintances are members of the movement may influence the focal individual’s beliefs in its value, and thereby also his/her propensity for joining the movement. Dissonance-based mechanisms (e.g. Festinger 1957) are also of potential importance in contexts such as these. If friends and acquaintances join a movement that the focal individual does not support, this is likely to produce dissonance. This in turn can set in motion a dissonance-reduction process that eventually may lead to a revision of the focal individual’s initial attitude towards the movement. In this manner, dissonance-based mechanisms may lead individuals to embrace and join movements because their friends and acquaintances have done so, even if they show no disapproval whatsoever of the individual remaining outside the movement. Finally, and as emphasized already by Olson (1965), an individual may incur various social and personal costs were he or she to remain outside a movement that most friends were part of. Depending on the specifics of the situation, these costs may range from slight feelings of discomfort from looks of disapproval to deep social wounds from being overtly ostracized. Avoiding – 115 –

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such costs may be an important motivational force leading individuals to join the same movements as their friends and acquaintances. In addition, most individuals enjoy spending time with their friends and acquaintances, and this may further motivate them to join them in their activities. Thus there are good theoretical reasons as well as a great deal of empirical research that would lead us to expect that an individual’s decision to join a movement is influenced by the actions of those with whom he or she interacts. How are these kinds of network-based social interdependencies likely to influence the movement itself? Is a movement likely to flourish, perish, or remain unaffected by being embedded in a social setting with certain structural properties? Although one might have thought that a macro-oriented discipline like sociology would be able to offer detailed answers to such a question, in fact we know very little about how networks affect the movement as such. We have strong reasons to believe that network properties influence individuals’ decisions, but as discussed above, knowledge about micro-level mechanisms like these will not in and of themselves inform us about the macrolevel outcomes they are likely to bring about. For this purpose a generative model is needed.

V. Modeling the growth pattern The generative model to be developed here will be simple and abstract. It will only include those elements believed to be particularly essential to the problem at hand. The model examines how the size of a movement is likely to be affected if the recruitment of new members is influenced by interactions between current and potential members, and if the exit of members is influenced by interactions between current and past members. At each point in time, individuals can be in one of three states: (1) they can be potential members of the movement, i.e., belong to the group of individuals who in principle can be recruited to the movement at that point in time; (2) they can be members of the movement; or (3) they can be non-recruitable exmembers of the movement. At any given point in time these states are mutually exclusive, but individuals can change state. In line with the findings of Snow, McAdam and others, it is assumed that the density of ties between current and potential members influences the recruitment of new members to the movement, and, in line with Sandell’s (1999) findings, it is assumed that the density of ties between past and present members influences the rate at which individuals leave the movement. – 116 –

Explaining the growth patterns of social movements

Although the interaction structure modeled here is rather simple, it has complex macro-level dynamics, and we need a formal model in order to understand the dynamics. The particular interaction structure considered here can be modeled as a system of ordinary differential equations defined as follows: dM = M (t ) P (t )d α − E (t )M (t ) gβ − M ( t) c dt dE = E (t ) M ( t) gβ + M ( t) c − E( t)δ dt dP = E (t )δ − M ( t) P(t )dα dt

where M(t) = number of movement members at time t, E(t) = number of ex-members at time t, P(t) = number of potential members at time t, d = average density of network ties between members and potential members (in the 0-1 range), g = average density of network ties between members and ex-members (in the range 0 - 1), α = the “attack rate” of the members, i.e., the number of potential members being recruited in relation to the number being contacted by a current member (in the range 0 - 1), β = the “attack rate” of the ex-members, i.e., the number of members being induced to leave the movement in relation to the number being contacted by an ex-member (in the range 0 - 1), c = the non-interaction based rate at which members leave the movement (in the range 0 - 1), and δ = the rate at which ex-members become potentially recruitable again. Network density is defined in the conventional way, i.e., as the average number of contacts an individual has with other individuals during a specific time period divided by the number of possible contacts. Although differential-equation models such as these do not model each actor’s behaviour, they are useful for analyzing the link between the micro – 117 –

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and the macro because they exactly describe the macro-level patterns that follow from the individual-level assumptions upon which the model is based. That is to say, the differential-equation model will predict the same social outcomes as would, for example, a large-scale agent-based model based on the same micro-level assumptions. Let us now look at these equations one at a time. The first equation says that the rate of change in the number of movement members (dM/dt) increases with the number of possible contacts between members and potential members. The number of unique dyads that can be formed between these two groups at any point in time is equal to the product of the number of members in each group, i.e., M(t)P(t). Only a fraction of these potential contacts is likely to be realized, however, and this fraction is given by the density of the social network. The number of realized contacts between movement members and potential members, therefore, will be equal to M(t)P(t)d. Through these actually realized contacts between movement members and potential members, some individuals will be recruited to the movement, and this number will be equal to M(t)P(t)dα. Contacts between members and ex-members will influence the rate of change in the number of members in a similar way. Out of the actually realized contacts between current and past members, E(t)M(t)g, a fraction (β ) will leave the movement. In addition, the model allows for members deciding to leave the movement irrespective of any influence of the ex-members. The number leaving the movement in this way is equal to cM(t). The second equation first of all restates what was said in the preceding paragraph, i.e., that the flow of individuals from the member category to the ex-member category is equal to E(t)M(t)gβ + cM(t). In addition, it states that ex-members can change their minds and become potentially recruitable again. It is assumed that this decision is not influenced by social interactions. The reason for this is that ex-members are likely to have more up-todate information than those in the potential member category and therefore they will not be much influenced by them. At any given time, a fraction of the ex-members (δ ) will change their minds and thus enter the potential member category again. The third equation simply sums up the changes already described. The rate of change in the number of potential members (dP/dt) increases with the flow of individuals from the ex-member category (E(t)δ) and decreases with the flow of individuals into the member category (M(t)P(t)dα). Figure 2 shows the macro-level dynamics implied by these micro-level assumptions for one particular set of parameter values (N = 500, P(0) = 498, – 118 –

Explaining the growth patterns of social movements

M(0) = 1, E(0) = 1, d = g = 0.01, and ι = β = δ = c = 0.1). The number of movement members first increases rapidly, then it falls and finally it stabilizes at its long-term equilibrium level.

Figure 2. Aggregate dynamics of a hypothetical social movement

To understand the dynamics of these kinds of systems, it is useful also to examine their equilibria. This is greatly simplified if, for the time being, we drop the distinction between network densities and attack rates and instead focus on the “effective transition parameterâ€? which is equal to the product of these two parameters, a = dÎą and b = gβ . What we are after thus is the long-term size of the social movement and how it is influenced by the various parameters of the model. We can find this by setting all three equations equal to zero and solving. After doing some straightforward but tedious math, we find that the long-term size of the social movement (denoted by M*) is equal to: M*

ac  Nab  aG  a 2 c 2  2 Na 2bc  2a 2 cG  N 2 a 2b 2  2 Na 2bG  a 2G 2  4abcG 2ab

(1) One additional, but trivial, equilibrium exists. This arises when the recruitment process never gets off the ground and no one ever moves from the potential member to the actual member category. Then, all individuals end up in the potential member category. This happens either when there

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is no movement “entrepreneur� who ignites the movement (M(0) = 0) or when a = 0 and b > 0 and δ > 0. In order to see what Equation 1 implies as far as the effects of networks on the size of the movement is concerned, it is instructive to focus on the pure case where c=0, i.e., where individuals are induced to leave the movement only through ties to ex-members. The equilibrium size of the movement then is equal to: M*

Nb  G  ( Nb  G ) 2 2b


If we assume that Nb≼ δ the expression can be further simplified and becomes: M* =

δ . b

The assumption that Nb≼ δ simply ensures that N ≼ M * , i.e., that there can never be more members then there are individuals in the system as a whole. If we now unpack b into its two constituent components, we find that the long-term membership level (M*) is simply given by: M* =

δ . gβ

The equilibrium size of the social movement thus increases with the rate at which ex-members change their minds and become recruitable again (δ), and it decreases with the density of the network connecting past to current members (g), and with the attack-rate of the ex-members (β).

VI. Empirical calibration of the generative model The dynamics of interactive systems like these can be rather sensitive to small changes in parameter values. Therefore it is essential to anchor the model in reality, and this is what empirical calibration is all about. As Coleman (1981) emphasized, it is important to distinguish between empirical calibration and empirical testing. To empirically test a theoretical model like this is far from straightforward. The model is not intended to be a fully realistic model of any specific social movement. It is meant to be a relevant model for understanding certain aspects of mobilization processes in general. Pointing out that a model like this deviates in some respects from empirical reality, is a rather pointless exercise. What we can do, however, is to – 120 –

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calibrate the model to reality by using a specific dataset to estimate the size of the unknown parameters. I would not consider this a particularly powerful “test” of the model however. The social movement that I will focus on here is a local Swedish temperance organization that was part of the Independent Order of Good Templars (IOGT). It was located in a Swedish parish called Husby-Rekarne some 100 kilometers west of Stockholm. The time period I am focusing on is 1897 to 1937 (see Jansson 1982 for a detailed description of the data). I will use the data on the annual inflow and outflow of members to estimate the parameters of the model. An optimization algorithm, the Levenberg-Marquandt algorithm, will be used to search for the combination of parameter values that leads to the smallest sum of squared deviations between the actual data points and those predicted on the basis of the model. The size of the relevant population, P(t) + M(t) + E(t), is assumed to be equal to 2500, which is the maximum population size of the parish during this time period. M(1897) is set at its actual value, 60, and E(1897) is assumed to be equal to 10, the number of members who left the movement during 1896. The software used to estimate the parameters is Model Maker 3 (see Walker 1997). The optimal parameter estimates found with this method were the following: a = 0.0003, b = 0.009, c = 0.08, and δ = 0.68. In Figure 3, the predictions of the model are compared with the actual data. As can be seen, the fit of the model is reasonably good (R2 = 0.46). The model also is able to capture some of the rather substantial membership fluctuations observed during this time period. Even though the model abstracts away from all specific historical events that occurred during this period, it does a reasonably good job of describing the longue durée of the movement.

Figure 3. The evolution of an IOGT movement in Husby-Rekarne. Theoretical predictions (−) and actual data (+). – 121 –

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Bearing in mind the illustrative nature of these analyses, what do these parameter values tell us? First of all, it shows that the “effective transition parameter” was about 30 times as high for the outflow as for the inflow (b = .009 and a = .0003). Most of this difference is likely to reflect differences in network densities. Since this was a rather small movement it seems likely that most exmembers and members knew one another. This means that the density of the network linking past and current members is likely to have been close to unity, and the b-parameter therefore directly reflects how effective the ex-members were in swaying members to leave the movement. A parameter value of .009 hence suggests that approximately 1 out of 100 ties between ex-members and members led to a member leaving the movement each year. If we assume that the members were equally effective in their interactions with potential members, this suggests that the density of ties between members and potential members was about .03 (≈ .0003/.009). Furthermore, the δ-estimate of .68 suggests that, on average, ex-members entered the ranks of the potentially recruitable about 1.5 years after they left the movement (.68–1 = 1.47). Models like these can be useful for performing what-if analyses. What would, for instance, be likely to happen with the long-term size of the movement if the networks linking potential, current, and past members to one another were altered? Inserting the estimated parameters into Equation 1, one finds that the implied long-term equilibrium size of the Husby-Rekarne movement was about 67 members. By changing the size of the networkrelated parameters we can get some sense of how changes in network densities are likely to affect the size of the movement (see Figure 4).

Change in Equilibrium Size





a b c


-20 -25

0 10 -10 Parameter Change %


Figure 4. Predicted changes in the equilibrium size of the movement due to changes in parameter values. – 122 –

Explaining the growth patterns of social movements

The results in Figure 4 suggest that a given change in the density of the network linking past and current members to one another (as captured by the change in the b-parameter) results in a much larger change in the equilibrium size of the movement than what a corresponding change in the network linking current and potential members (the a-parameter) results in. In fact, were both the a- and the b-coefficients reduced by 25 percent, these results suggest that the equilibrium size of the movement would increase by almost 20 members (from 67 to 85 members). These results are not as counterintuitive as they may appear, however, since the absolute size of a and b differ. A 25 percent change therefore represents rather different changes in absolute terms. These results also suggest that the size of a movement is likely to be much affected by the rate at which ex-members become potentially recruitable again. This is indicated by the steep gradient of the line which describes the effects of changes in the δ-parameter.

VII. Concluding remarks The reason for presenting these analyses is not that I believe that the details of these results can be generalized to all sorts of social movements. Nor do I believe that the model as such is the ideal model for analyzing the evolution of social movements. The main reason is a methodological one, to bring home the point that empirical results that refer exclusively to micro-level processes rarely allow us to predict what the macro-level outcomes will be. We know from a range of different studies that individuals’ decisions whether or not to join a social movement often is influenced by the extent to which they interact with movement members. Research on the role of networks in recruiting individuals to social movements has, at least in part, been motivated by a belief that high-density networks benefit social movements (e.g. Tilly 1978). But, as suggested here, the link between micro and macro is much more complex than this, and changes in network densities may hinder as well as support a social movement. The way in which interactions at the micro-level are likely to influence the size of a social movement depends upon the relative network densities between different sub-groups, the extent to which individuals in different groups influence one another, and the size of these various groups. To get a handle on how these various factors are likely to jointly influence the growth trajectory of a movement requires a generative model, and the model developed here is one example of such a model. John Maynard Smith (1993) once noted that the major contribution made by mathematics to science may not primarily have been to facilitate the – 123 –

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drawing of conclusions from premises, but rather in bringing out structural similarities between disparate systems. The type of model being used here exemplifies Maynard Smith’s thesis. It is a close relative to models used in biology and epidemiology to analyze the spread of infectious diseases (see Anderson and May 1991, Murray 1993), and it appears directly applicable to the analysis of many other social processes that follow a similar logic, such as neighborhood social problems as discussed by Crane (1991) and the diffusion of various cultural phenomena as discussed by Sperber (1996). At sufficiently high levels of abstraction, the logic of many of the processes studied by epidemiologists, biologists, and sociologists are virtually isomorphic. Although one should always be on guard against unwarranted analogies between natural and social processes, this is nevertheless a comfort for an under-formalized discipline like sociology. Formal models required for analyzing social processes rarely need not to be invented from scratch.

Acknowledgements I wish to thank Christofer Edling, Diego Gambetta, John Goldthorpe, Jenny Hedström, Fredrik Liljeros, Åke Svensson, and Yvonne Åberg for valuable comments and suggestions on an earlier version of this paper.

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Skog, O.-J. (1988), “Testing Causal Hypotheses about Correlated Trends: Pitfalls and Remedies”, Contemporary Drug Problems 15: 565-607. Snow, D.A., Zurcher, L.A. and Ekeland-Olson, S. (1980), “Social Networks and Social Movements: A Microstructural Approach to Differential Recruitment“, American Sociological Review 45: 787-801. Sperber, D. (1996), “The Epidemiology of Beliefs,” chapter 4 in D. Sperber (ed.), Explaining Culture: A Naturalistic Approach. Oxford: Blackwell. Tilly, C. (1978), From Mobilization to Revolution. Reading: Addison-Wesley. Walker, A. (1997), Model Maker 3: User Manual. Oxford: Cherwell Scientific Publishing Ltd. Wright von, G.H. (1971), Explanation and Understanding. Ithaca: Cornell University Press.

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