Partial participation towards collective action: To stifle or instigate

Abstract

In this paper we extend the Granovetter threshold model with partial participation towards a collective action. That is, agents may partake by conducting an action that is less costly than the ultimate collective action, but costly enough to signal a commitment to the cause. We show that it is not just the exact distribution of thresholds, but also the distribution of available actions that determines whether a collective action will be achieved. We suggest and prove propositions for how both an inventive “activist” and a “dictator” may strategically change the signaling value of existing actions, or introduce new ones, in order to either instigate or stifle collective action. Applying the theory to revolutions, we argue that new technology can play a role beyond that of communication and synchronization, viz. that of adding modes of partial, less arduous, participation.

Keywords

Threshold model collective action partial participation uprising revolution social media

Introduction

A collective action problem is a situation in which multiple individuals would all benefit from a certain action, but no single individual is willing and able to undertake and solve it alone. An understudied fact in the collective action literature is that there is often more than just a single action available for an individual to move the group towards collective action. Our contribution in this paper is a formal model designed with this fact in mind.

“There are many types of collective action, and they cannot all be captured with the same formal model.” (Oliver, 1993). In this paper, we will introduce a variation of what Oliver calls a “simple threshold model”. This allows us to model situations where an individual’s willingness to partake depends on how many of the others are partaking. Many social situations match this description, and among the classic examples are: applause (Lupyan and Rifkin, 2003), residential segregation (Granovetter and Soong, 1988), the filling of a dance floor (Giudicati et al., 2013), the adoption of social norms (Bicchieri, 2006) or new technology (Wejnert, 2002), and the joint effort to topple a dictator (Tilly, 1985). Revolutionary uprisings will serve as our running example, partly to make the discussion more concrete, but also to make a small contribution to the existing literature on uprisings.

The model to be presented is an extension of Mark Granovetter’s threshold model (Granovetter, 1978; Granovetter and Soong, 1983). Following Granovetter, the decision to partake in a collective action, or not, is not necessarily modeled as a reasoned choice by the individual. Instead, participation by an individual is determined by the simple question: Has the current participation level, i.e. the number of others already participating, surpassed the relevant threshold where you join as well? The original model remains agnostic to why an individual holds a certain threshold, as do ours. Instead, the focus is on how individual thresholds aggregate. Granovetter shows how participation may feed more participation, and thus how aggregation may generate a “bandwagon effect”: a single instigator causes a few to join, the few cause others to join, the others compel yet others, and so on until a successful collective action been achieved. Whether or not bandwagoning ensues depends on the exact distribution of thresholds in the population. The main result of the Granovetter (1978) paper is that even minor perturbations to these distributions may halt bandwagoning altogether.

In the original model, as already noted, an individual at each time step chooses to take part, or not. Our extension presents individuals with a finer structure of actions, which opens up partial participation, an aspect omnipresent in the real world. In the case of popular uprisings, taking part in the pivotal military action is far from the only way to partake, e.g. anonymous social media, face-to-face agitation, and protest demonstration.

To formalize partial participation we introduce pre-actions: Let a simple action be an action that does not need to be collectively orchestrated to make a difference. That is, a single individual conducting a simple action signals commitment to the collective action no matter what the others do.¹ Let a pre-action be either a simple action or a bundle of simple actions. That is, if say an individual first agitated anonymously on social media, and then continued to agitate but also donated a sizable donation towards the cause; she would first take the simple pre-action, $a_{i}$ , implying anonymous agitation, and then escalate to the pre-action, a_j, that includes both anonymous agitation and a donation. Bear in mind that escalation does not need to imply that the individual takes a pre-action that just extends the previous bundle; it could just as well imply switching from a large bundle to a pre-action consisting of only a single simple action, such as in our example, replacing the agitation and donation to only picking up arms. The median effort level of a pre-action is assumed to be lower than that for the full collective action, making it able to serve as a stepping stone in the stairway to collective action.

Our model lets us explore two interesting questions.

If, and when, will a set of pre-actions catalyze bandwagoning such that it causes full collective action?

If, given the power to change the signaling effects of pre-actions, what changes need to be made to halt, or instill, bandwagoning to achieve collective action?

For the example of popular uprisings, the first question sheds light on the importance of innovation in modes of participation, and the second question provides the defender of the status quo with hints for how to stifle uprisings.

Model

A finite population, P, is assumed. In the Granovetter model, individuals have a single choice at each time step: action or inaction. Here we extend the set of actions available such that it also includes pre-actions. It will be convenient to order them, such that the action set consists of $a_{0}$ = “inaction”, $a_{m}$ = “full action”, and the sequence of pre-actions $a_{1}, \dots, a_{m - 1}$ in order of increasing signal value (to be defined below).

We shall think of individuals’ decisions as making a trade-off between the expected “effort” of taking an action (capturing all the forces that create resistance to acting) and the willingness to join the cause if the others are sufficiently committed to it. Each individual, however, has a subjective expectation of how much effort is required by herself to do the action next time. Let $f_{k} (a_{i})$ denote individual $k$ ’s perceived subjective effort level for conducting action $a_{i}$ . Let effort be measured on a scale normalized such that the median expectation of the perceived subjective effort required for inaction and full collective action is $0$ and $1$ , respectively.

By our definition of pre-actions, we have assumed that the effort will signal commitment. Our premise is that taking effort signals commitment. Because individuals vary in how much effort they think various actions will take, some aggregation over the population must be assumed. Our assumption is that the signal value $s (a_{i})$ of action $a_{i}$ is the median perceived effort of this action in the population; an operationalization of how much perceived effort is commonly believed to have been required by “people in general”. In particular, this means that the signal value of full action is $s (a_{m}) = 1$ and that the signal value of inactivity is $s (a_{0}) = 0$ . Intermediate actions are assumed to have intermediate signal values

0 = s (a_{0}) ⩽ s (a_{1}) ⩽ \dots ⩽ s (a_{m - 1}) ⩽ s (a_{m}) = 1 .

The relation between signals and the distribution of effort levels is depicted in Figure 1.

Individuals must somehow gauge the commitment of the population as a whole. We will assume that they do this by calculating the average signal value of the various actions currently taken in the population. Letting $α_{t}^{k}$ be the action chosen by individual $k$ at time $t$ . The societal commitment level at time $t$ is then

C_{t} = \frac{1}{| P |} \sum_{k \in P} s (α_{t - 1}^{k}) .

(1)

Next, each individual $k$ has a participation threshold $T_{k}$ between $0$ and $1$ per collective action. This threshold is modulated for each action $a_{i}$ in accordance with its subjectively perceived level of effort required, $f_{k}$ , such that for individual $k$ the de facto threshold is $T_{k} f_{k} (a_{i})$ . The escalation criterion for individual $k$ , that is the criterion that need to hold for $k$ to escalate to action $a_{i}$ at time step $t + 1$ where $s (a_{i}) > s (α_{t}^{k})$ , is that the societal commitment level is greater or equal to her de facto threshold,

C_{t} ⩾ T_{k} f_{k} (a_{i}) .

(2)

Note that restricting the action set to ${a_{0}, a_{m}}$ and letting $f_{k} \equiv 1$ for all $k$ gives us the dynamics of the Granovetter model.

Escalation to collective action

We define collective action to be achieved if at least half the population takes full action. We shall now demonstrate that the existence of pre-actions at suitable signal levels will lead to bandwagoning and full escalation under certain conditions. Let an “activist” be someone with the ability to invent actions with any signal value. Assume that for the action set ${a_{0}, a_{m}}$ collective action will not be achieved in our population. Suppose also that there is an effortless pre-action $a_{1}$ (or one could be invented) such that it takes effort for the median individual (i.e. it has non-zero signal value), but takes no effort for some individuals. Further assume that such an action $a_{1}$ is enough to set in motion a bandwagoning such that at least half the population take (at least) action $a_{1}$ . These criteria are enough to guarantee that invention of a series of pre-actions will lead a population for whom the threshold $T_{k} < \frac{1}{2}$ to collective action.

Proposition 1 If the threshold $T_{k}$ is less than a half for each individual $k$ , and there exists an action $a_{1}$ with non-zero signal value that at least half the population will eventually take, then inventing a finite sequence of actions $a_{2}, a_{3}, \dots$ with increasing signal values $s (a_{i}) = 1 / (2 T)^{i - 1} s (a_{1})$ will achieve the final collective action.

Proof. Let the activist introduce actions a₂, a₃, … with signal values

s (a_{i}) = \frac{1}{{(2 T)}^{i - 1}} s (a_{1}), for i > 2 .

(3)

We will show that at least half the population escalate from one action $a_{i}$ to (at least) the next $a_{i + 1}$ at each time step; we may thus simplify the notation by using t $t$ as an index for $a_{i}$ too.

The proof will be by induction. The base case follows by assumption: At least half the population will escalate at $t = 1$ to action $a_{1}$ .

It now remains to show that for any time step $t > 1$ , that if at least half the population participated in action $a_{t}$ a_t then at least half the population will escalate to $a_{t + 1}$ at time $t + 1$ .

The median effort level for $a_{t + 1}$ is given by equation (3) and can also be written in recursive form,

s (a_{t + 1}) = \frac{1}{{(2 T)}^{t}} s (a_{1}) = \frac{1}{2 T} s (a_{t}) .

(3a)

Hence, using the assumption that $T_{k} < 1 / 2$ and recalling that the signal value is the median of all effort levels, the escalation criterion (equation (2)) will hold for half the population as

C_{t + 1} ⩾ T s (a_{t + 1}) .

Using equation (3a), we can rewrite the right-hand side as

T s (a_{t + 1}) = T \frac{s (a_{t})}{2 T} = \frac{s (a_{t})}{2} .

Our induction assumption is that at least half the population conducts $a_{t}$ at time $t$ , implying a societal commitment level at $t + 1$ of

C_{t + 1} ⩾ s (a_{i}) / 2 .

(4)

the escalation criterion thus holds. By induction from the base case, the premise that at least half the population will eventually take action $a_{1}$ , it now follows that at least half the population will keep escalating (not necessarily the same individuals) until full collective action is achieved.

The societal commitment escalation at each time step is constant, and thus tends to infinity, ensuring that we eventually reach the societal commitment level of $1$ , i.e. full collective action. □

Participation in pre-actions thus adds up to an aggregated societal commitment level. An individual participates in a pre-action if her de facto threshold is lower than the current societal commitment level. The pre-actions, as we show in Proposition 1, can act as a “stairway” to full collective action. Varying the subjective efforts required, and thus the signaling value, this makes collective action achievable in cases where it otherwise would not have been.

One may object that Proposition 1 suggests that an unreasonable number of cases would bandwagon to success. For example, consider a population of wealthy individuals with a set of pre-actions ${a_{x}}$ . Each action $a_{x}$ is a donation of $ $x$ dollars to the collective cause. Intuitively, more money should imply more signaling. Further, the amount of money donated could be argued to be on a continuum. If so, Proposition 1 implies that this set of pre-actions, given the right initial conditions, will always bandwagon to achievement. This seems not to be the case, we thus suggest two caveats to the description: First, cognitively there may not be a difference between the signal value of a donation of $1 million dollars, and a donation of $1 millon dollars and 1 cent. Secondly, escalation by minuscule signaling values is in almost all cases impractical and improbable due to the transaction costs of conducting all the pre-actions. Note that neither of these caveats gets represented in the model.

What a dictator can do

In this section, we will no longer concern ourselves with an activist extending the action set to achieve collective action. The assumption here is instead that we have a fixed set of actions ${a_{0}, \dots, a_{m}}$ and a population with effort levels and thresholds such that it will escalate to full collective action. In contrast to the “activist” who schemed to achieve collective action, we will here consider a “dictator” scheming to stifle it. Let the “dictator” have the capacity to change effort levels of existing actions, and consequently their signaling values. We will show that the dictator may bring a halt to escalation, and thereby successfully stifle collective action, by both increasing and decreasing effort levels.

First, let a crucial action $a_{*}$ be an action such that if it were to be removed from the fixed action set, the full collective action would not be achieved. Also, let the set of pivotal individuals for a crucial action $a_{*}$ be the set of individuals for whom the escalation criterion eventually would fail conclusively if $a_{*}$ were to be removed.

Proposition 2 If there is at least one crucial action, a dictator may halt escalation to full collective action by raising the required effort levels for a crucial action $a_{*}$ .

Proof. Raising the pivotal individuals’ effort levels for the crucial action such that the escalation criterion fails is always possible. At the extreme, the dictator may set the new effort level for each pivotal individual $k$ to be equal to the full action, ${f^{'}}_{k} (a_{*}) : = f_{k} (a_{m})$ . Since the action was crucial, this modification renders the escalation criterion false for all pivotal individuals k. I.e. C_t < T_k f′_k(a_*), for all t. This hence halts escalation towards full collective action.

Raising the effort levels, ${{f^{'}}_{k} (a_{i})}$ , or metaphorically “raising the tread of a step in the stair”, may make individuals refrain from taking action as the societal commitment level no longer fulfills the escalation criterion (as we saw in Proposition 2). Raising the effort levels would however also increase the signaling value of an action. Thus, if the new and higher effort levels will not make individuals refrain, they will instead raise the societal commitment level in the next time step, increasing the likelihood of further escalation. This leads us to our next proposition.

Proposition 3 If there is at least one crucial action, a dictator may halt escalation to full collective action by lowering the required effort levels for a crucial action $a_{*}$ .

Proof. Lowering efforts levels such that the escalation criterion fails is always possible. The dictator may, at the extreme, modify the effort levels such that the median effort level for the crucial action equals that of inaction, $s^{'} (a_{*}) : = s (a_{0})$ . Implying that the crucial action no longer acts as a stepping stone. The crucial action is thus effectively removed, and full collective action will not be achieved. □

This is a counterintuitive result – by lowering effort levels, the collective action is stifled. The explanation, of course, is in the signaling value. As the effort of the crucial action is lowered, so is its signaling value, to the point where the action no longer functions as a stepping stone.

It is therefore sometimes in a dictator’s interest to lower the effort levels, ${{f^{'}}_{k} (a_{i})}$ , or “lower the tread of a step in the stair”, such that the signaling from the already achieved actions will contribute less signaling value to the societal commitment, and thereby possibly prevent further escalation.

In other words, harsher punishments for certain acts to deter revolutionaries can be counterproductive; because if the actions are still committed, the punishments will just make the commitment signal stronger, thus increasing the perceived level of societal commitment, pushing more people over their thresholds for action. For the metaphor, this implies that a dictator wants to assure that the stairway has steps configured such that the shortest riser is as tall as possible.

Propositions 2 and 3 both assume the existence of a crucial pre-action $a_{*} .$ In the general structure of the model introduced in the “Model” section, it is not guaranteed that such an action exists a priori. However, a dictator who controls effort levels may always make a pre-action crucial as she can go to the extreme and modify all the other effort levels such that all but the crucial action in spe share a median effort level with either inaction or full action. That is, such that $s (a_{i}) = s (a_{0})$ or $s (a_{j}) = s (a_{m})$ for all $i, j$ not being the crucial action.

The two propositions essentially show that a dictator may make a riser taller, either by decreasing the signal value of its lower step or by increasing that of its upper step, as illustrated in Figure 2. In the proofs of the propositions we go to extremes; most often much smaller modifications in signal value would suffice. The exact details of a minimal modification will, however, depend on the details of the population’s threshold and effort levels.

Discussion

In this paper, we introduced a simple deterministic model based on the Granovetter threshold model. The modification opens up partial participation, and we explore how this interacts with the bandwagoning phenomena of the original model. To operationalize partial participation we introduce pre-actions.

The model was motivated by an interest in how new technology affects social uprisings by giving rise to new ways to participate in collective action. The rest of the discussion will reconnect the model to this literature.

The societal commitment level

How reasonable is the societal commitment level $C_{t}$ used in the model? Clearly, it is not the case that each and every member of a society perceives such a thing non-ambiguously and inter-subjectively. Nevertheless, in the case of revolutionary upheavals, the literature does suggest that the Internet creates a new communicative space: a Verbindungnetzschaft (Dartnell, 1999), a virtual (Benmamoun et al., 2012), global (Kyriakopoulou, 2011) or amplified (Nanabhay and Farmanfarmaian, 2011) public sphere that speeds up communication, enables organization of protests, and encourages media coverage. Against this background, it seems reasonable to model a societal commitment level that is a function of individual social signaling functions.

Dictator strategies

Even though the dictator can manipulate the effort functions $f_{k}$ to her advantage, Propositions 2 and 3 show that it is not always clear whether she should adjust it upwards or downwards.

To some extent, this mirrors the complexity of real world events such as in the Egyptian escalation. The Egyptian leader Mubarak “raised the tread” as he banned content, platforms (e.g. Facebook and Twitter) and infrastructure (e.g. cell phone and Internet services) (Dunn, 2011). However, in the end, Mubarak’s decision to cut Internet services did not save him — indeed, some argue that it accelerated his downfall (Hassanpour, 2011). Another example, where “raising the tread” has had counterintuitive consequences is Chinese Internet censorship. Rumors on the Internet are outlawed as “cyber crimes” (Zhao, 2009) and made punishable by three-year sentences (Reuters, 2013). The laws themselves, however, have contributed to shaping an online environment that is uniquely conducive to rumors (Ma, 2008).

However, manipulation of pre-action thresholds need not at all be interpreted within the framework of revolutions. For example, the original Granovetter threshold model has inspired research into many different areas where “vicious circles” are prevalent, e.g. organized crime (Lavezzi, 2014), low tax morale (Lisi and Pugno, 2011), and adverse individual behavior in welfare states (Lindbeck, 1995). We conjecture that the steps of such vicious circles could sometimes be interpreted as pre-actions in our sense and that analysis of efforts to break such circles could thus meaningfully be conducted in terms of manipulation of pre-action thresholds.

Activist strategies

There is a large body of literature devoted to the innovative use of technology by opposition and protest movements, in particular in authoritarian societies. These innovations can be likened to the actions of the inventive “activist” in Proposition 1. Interesting examples of how the Internet can be used to circumvent censorship, and metaphorically “how new steps are added to the stairway”, include Peru in the 1990s (Dartnell, 1999) and Malaysia and Singapore in the 2000s (Abbott, 2012; Ahmad et al., 2012). More recently, examples from the Arab spring abound, including Diani’s argument that information and communication technology (ICT) can help circumvent surveillance and repression, as long as it is not overly sophisticated (Diani, 2011). Too high sophistication would, in the model, imply that the action would require too much effort for too many of the individuals $k,$ i.e. for the action $a_{i}$ , $f_{k} (a_{i})$ is too large. Alqudsi-Ghabra stresses the role of creativity, or in our terms “inventiveness”, in order to escape censorship: if Facebook was censored, Twitter was used instead (Alqudsi-Ghabra, 2012). Eriksson et al. (2013) elaborate on several more sophisticated inventions used throughout the Arab spring: When the Tunisian Internet Agency blocked the HTTPS protocol in order to be able to steal user passwords through so-called “man in the middle attacks”, activists quickly distributed a small program to delete the attack code, enabling safe browsing of the Internet. However, most users were not able to download and use the patch. During the Egyptian Internet shut-down, activists convinced Internet Service Providers in France, Sweden, the Netherlands and other countries to restart old modem banks no longer in use. Dial-up connections to these enabled Egyptians to access the Internet. Several companies donated the service fees, facilitating free calls. Google also initiated the Speak2Tweet-service; a regular phone number with an answering machine, where the messages read were automatically tweeted with the tag #Egypt (Eriksson et al., 2013). In much of the literature, the role ascribed to technological innovations is aiding the spread of the word and making coordination more feasible. Proposition 1 suggests that part of technological effects also could be explained by bandwagoning of the population’s societal commitment.

Taken together, the strategies of dictators and activists set the stage for a race between them. In our model, this race takes a form where the dictator tries to ensure that one high riser will halt escalation, and where the activists try to add new steps to ease climbing the highest riser. This bears a striking resemblance to the literature: Diamond (2010) describes the technological race between democrats who attempt to circumvent Internet censorship and dictators who attempt to improve it. Howard and Hussain (2013) argue that any assessment of the revolutionary impact of ICT must account for the context of countermeasures employed by the regime. They point out that Saudi Arabia, Bahrain, and the United Arab Emirates — countries unaffected by the Arab spring — all employed sophisticated systems for surveillance and censorship (Howard and Hussain, 2013). Such observations have led Bryant (2012) to argue that technology is neutral and can help both revolutionaries and dictators.

However, activist innovation of pre-actions needs not at all be interpreted within the framework of revolutions. For example, the original Granovetter threshold model has inspired research into the susceptibility of individuals to adopt products marketed (Aral and Walker, 2012). Continuing that line of reasoning into our extended model, companies could be viewed as activists, constantly inventing pre-actions such as liking a product on Facebook, sharing a product user-experience with friends, or becoming a member of a product or brand club, all designed to facilitate the final action of buying. The original Granovetter threshold model has also inspired research into how organizations can elicit suggestions for action from external contributors (Dahlander and Piezunka, 2014). Following this literature, pre-actions include organizations submitting their own suggestions in order to trigger the final action suggestions from others. Yet another example from the literature has to do with how new technology enables changes in how people within organizations communicate with each other (Leonardi, 2013). Inspired by this literature, usage of a particular feature in a software tool can be seen as a pre-action on the way to the final action of a new communication pattern.

Conclusion

In the wild, phenomena classified as collective actions often show more refined agents participation, with further options than just to full participate, or not. In this paper, we considered how various modes of participation interact with the escalation dynamics of collective actions.

To do this, we developed an extension to the classic threshold model of Mark Granovetter. The extension introduces a finer structure of actions, allowing us to think about partial participation in collective actions.

The new model remains a threshold model. The measure of the number of participants is replaced with an aggregate of the various forms of participation, a sum of the commitment signals of the actions taken. The signal values are in turn given by the median effort level required to take that action. This aggregate measure is then compared to the individual threshold for a specific action. This per-action-threshold is given by the individual’s overall threshold modulated by how much effort she perceives the action would require of her.

Comparing our proposed model with Granovetter’s original single-action model is not straightforward. Note, however, that both can be used to model the same phenomenon but at different levels of granularity. Thus, our proposed model can capture more fine-grained dynamics, but at the cost of more model complexity, whereas the original Granovetter model in its elegant simplicity may miss important aspects of the relevant dynamics. For example, if a revolution is modeled as a single action in the original Granovetter model, it means that all kinds of pre-actions (to use our terminology) are implicitly assumed and allowed. However, if a revolution is modeled as a single action in our extended Granovetter model, it means something entirely different: all kinds of pre-actions are explicitly ruled out.²

We use the new model to show that the opportunity to participate partially can create a stairway to the full collective action.

We show that, under some assumptions, a population will be bandwagoning towards achieving full collective action solely by the introduction of more modes of participation. We also consider how someone with an interest in stifling collective action and the power to alter how much effort actions take, may create taller risers by either lowering the lower step or raising the upper one.

In the discussion, we relate these results to the literature on the importance of innovation and technology in revolutionary uprisings, particularly the Arab spring.

Footnotes

Funding

This research received no specific grant from any funding agency in the public, commercial, or not-for- profit sectors.

Notes

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