Mapping the "structure of cooperation": Adding the time dimension and thinking about further analyses

 

In October 2020 I wrote the first blog of the same name, based on some experiences with analysing the results of a ParEvo exercise. (ParEvo is a web assisted participatory scenario planning process).

The focus of that blog posting was a scatter plot of the kind shown below. 

Figure 1: Blue nodes = ParEvo exercise participants. Indegree and Outdegree explained below. Green lines = average indegree and average outdegree

The two axes describe two very basic aspects of network structures, including human social networks. Indegree, in the above example, is the number of other participants who built on that participant's contributions. Outdegree is the number of other participant's contributions that participant built on.  Combining these two measures we can generate (in classic consultants' 2 x 2 matrix style!) four broad categories of behavior, as labelled above. Behaviors , not types of people, because in the above instance we have no idea how generalisable the participants' behaviors are across different contexts. 

There is another way of labelling two of the quarters of the scatter plot, using a distinction widely used in evolutionary theory and the study of organisational behavior (March, 1991, Wilden et al, 2019). Bridging behavior can be seen as a form of "exploitation" behavior, i.e., it involves making use of others prior contributions, and in turn having one's contributions built on by others.  Isolating behavior can be seen as a form of "exploration" behavior, i.e., building storylines with minimal help from other participants.  General opinion suggest that there is no ideal balance of these two approaches, rather it is thought to be context dependent. But, in stable environments exploitation is thought to be more relevant whereas in unstable environments, exploration is seen as more relevant.

What does interest me is the possibility of applying this updated analytical framework to other contexts. In particular to: (a) citation networks, (b) systems mapping exercises. I will explore citation networks first. Here is an example of a citation network extracted from a public online bibliographic database covering the field of computer science. Any research funding programme will be able to generate such data, both from funding applications and subsequent research generated publications.

Figure 2: A network of published papers, linked by cited references

Looking at the indegree and outdegree attributes of all the documents within this network the average indegree, and outdegree, was 3.9. When this was used as a cutoff value for identifying the four types of cooperation behavior, their distribution was as follows: 

• Isolating / exploration = 59% of publications
• Leading = 17%
• Following = 15%
• Bridging / exploitation = 8%

Their location within the Figure 2 network diagram is shown below in this set of filtered views.

Figure 3: Top view = all four types, Yellow view = Bridging/Exploitation, Blue = Following, Red = Leading, Green = Isolating/Exploration

It makes some sense to find the bridging/exploitation type papers in the center of the network, and the isolating/exploration type papers more scattered and especially out in the disconnected peripheries. 

It would be interesting to see whether the apparently high emphasis on exploration found in this data set would be found in other research areas. 

The examination of citation networks suggests a third possible dimension to the cooperation structure scatter plot. This is time, as represented in the above example as year of publication. Not surprisingly, the oldest papers have the higher indegree and the newest papers have the lower. Older papers (by definition, within an age bounded set of papers) have lower outdegree compared to newer papers).  But what is interesting here is the potential occurrence of outliers, of two types: "rising stars" and "laggards". That is, new papers with higher than expected indegree ("rising stars") and old papers with lower than expected indegree ("laggards", or a better name??), as seen in the imagined examples (a) and (b) below.

Another implication of considering the time dimension is the possibility of tracking the pathways of individual authors over time, across the scatter plot space. Their strategies may change over time. "If we take the scientist .. it is reasonable to assume that his/her optimal strategy as a graduate student should differ considerably from his/her optimal strategy once he/she received tenure" ( Berger-Tal, et al, 2014) They might start by exploring, then following, then bridging, then leading.

Figure 4: Red line = Imagined career path of one publication author. A and B = "Rising Star" and "Laggard" authors

There seem to be two types of opportunities present here for further analyses:

1. Macro-level analysis of differences, in the structure of cooperation across different fields of research. Are there significant differences in the scatter plot distribution of behaviors? If so, to what extent are these differences associated with different types of outcomes across those fields? And if so, is there a plausible causal relationship that could be explored and even tested?  
2. Micro-level analysis of differences, in the behavior of individual researchers within a given field. Do individuals tend to stick to one type of cooperation behavior (as categorised above). Or is their behavior more variable over time? If the latter , there any relatively common trajectory? What are the implications for these micro-level behaviors for the balance of exploration and exploitation taking place in a particular field?