Noncooperation and the Latency of Weak Ties

As Centola and Macy summarize, the key insight of Granovetter’s seminal 1973 work (Granovetter, 1973) is that ties which are “weak in the relational sense – that the relations are less salient or frequent – are often strong in the structural sense – that they provide shortcuts across social topology” (Centola & Macy, 2007). While this remains an important sociological finding, there are important reasons to be wary of generalizing too far: such ‘weak ties’ may not be sufficient for diffusion in complex contagion (Centola & Macy, 2007) and identification of such ties is highly dependent on how connections are defined and measured (Grannis, 2010).

Furthermore, recent studies probing just how far ‘the strength of weak ties’ can be taken allude to another underexplored concern: the latency of ties. For example, Grannis points to the oft glossed-over result of Milgram’s small world experiment (Milgram, 1967): 71% of the chains did not make it to their target. As Milgram explains, “chains die before completion because on each remove a certain portion of participants simply do not cooperate and fail to send the folder. Thus the results we obtained on the distribution of chain lengths occurred within the general drift of a decay curve.” Milgram and later Dodds et al. (Dodds, Muhamad, & Watts, 2003) correct for this decay by including in the average path length an estimation of how long uncompleted paths would be if they had in fact been completed. For his part, Grannis argues that the failure caused by such noncooperation is exactly the point: “it calls into question what efficiency, if any, could be derived from these hypothesized, noncooperative paths” (Grannis, 2010).

I call this a problem of latency because one can imagine that social ties aren’t always reliably activated. Rather, activation may occur as a function of relationship strength and task burden, or may simply vary stochastically. In their global search email task, Dodds et al. find that only 25% of self-registered participants actually initiated a chain, whereas 37% of subsequent participants – those who were recruited by an acquaintance of some sort – did carry on the chain (Dodds et al., 2003). They attribute this difference to the very social relations they are studying: who does the asking matters.

In their survey of non-participants, the authors further find that “less than 0.3% of those contacted claimed that they could not think of an appropriate recipient, suggesting that lack of interest or incentive, not difficulty, was the main reason for chain termination.” Again, this implies that not all asks are equal – the noncomplying participants could have continued the chain, but they chose not to. In economic terms, it seems that the activation cost – the cost of continuing the chain – was greater than the reward for participating.

One can imagine similar interactions in the job-search domain. Passing on information about a job-opening maybe relatively low-cost while actively recommending a candidate for a position may come with certain risk (Smith, 2005). In many ways, the informational nature of a job search is reminiscent of ‘top-of-mind’ marketing: it is good if customers choose your product when faced with a range of options, but ideally they would think of you first; they would chose to purchase your product before even being confronted with alternatives. In the job-search scenario, unemployed people are often encouraged to reach out to as many contacts as they can, in order keep their name top-of-mind so that these ‘weak ties’ – who otherwise may not have thought of them – do forward information when learning of job openings. Granovetter does not examine the job search process in detail, but his findings – that among people who found a new job through a contact, 55.6% saw that contact occasionally while another 27.8% saw that contact only rarely (Granovetter, 1973) – imply that information was most likely diffused by a job-seeker requesting information. In this case, the job seeker had to activate a latent weak tie before receiving its benefit.

Arguably, the concept of latency is built into the very definition of a weak tie – weak ties are weak because their latency makes them easier to maintain than strong, always-active ties. Yet, the latency of weak ties, or more precisely, their activation costs, are generally not considered. In his detailed study of three distinct datasets, Grannis finds that a key problem in network interpretation is that connections’ temporal nature is often over looked (Grannis, 2010). I would argue that a related challenge is that the observed relations are considered to always be active. Using Grannis’ example, there is nothing inherently wrong with the suggestion that ideas may flow from A to C over the course of 40 years; the problem comes in interpreting this as a simple network where C’s beliefs directly trace to A. Indeed, in the academic context, it’s quite reasonable to think that an academic ‘grandparent’ may influence one’s scholarly work – but that influence comes through in some ideas and not others, it comes through connections whose strength waxes and wanes. To consider these links always present, and always active, is indeed to neglect the true nature of the relationship.

Ultimately, Grannis argues that the core problem in many network models is that the phase transitions which govern global network characteristics are sensitive to local-level phenomena: if the average degree is measured to be 1, there will be a giant component. Given this sensitivity, it becomes essential to consider the latency of weak network ties. A candidate who doesn’t activate weak ties may never find a job, and a message-passing task for which participants feel unmotivated may never reach completion. In his pop-science article, Malcolm Gladwell argues that some people just feel an inherent motivation to maintain more social ties than others (Gladwell, 1999). Given such individual variation in number of ties and willingness to activate ties, it seems clear that the latency of weak ties needs further study, otherwise, as Grannis warns, our generalizations could lead to “fundamental errors in our understanding of the effects of network topology on diffusion processes” (Grannis, 2010).

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Centola, D., & Macy, M. (2007). Complex contagions and the weakness of long ties. American journal of sociology, 113(3), 702-734.

Dodds, P. S., Muhamad, R., & Watts, D. J. (2003). An experimental study of search in global social networks. Science, 301(5634), 827-829.

Gladwell, M. (1999). Six degrees of lois weisberg.

Grannis, R. (2010). Six Degrees of “Who Cares?”. American journal of sociology, 115(4), 991-1017.

Granovetter, M. S. (1973). The strength of weak ties. American journal of sociology, 1360-1380.

Milgram, S. (1967). The small world problem. Psychology today, 2(1), 60-67.

Smith, S. S. (2005). “Don’t put my name on it”: Social Capital Activation and Job-Finding Assistance among the Black Urban Poor American journal of sociology, 111(1), 1-57.

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