disc and paper

Week 5

An Introduction to Systems Analysis

Complex Systems

We all come from and live in complex systems – cultures, economies, political organizations, families, and so on – but one of the constant themes coming out of research in the social sciences is that the level of complexity in our world as a whole is increasing at an exponential rate.

When we talk about a complex system, we are talking about a network of diverse, connected, interdependent, adaptive parts (Mitchell, 2009). We can contrast these characteristics with those of a complicated system that may have diverse parts working together, but they cannot to change.

For example, imagine a watch: it has many diverse parts, connected to each other, and operating in tandem to keep time, but you cannot remove any of its parts without causing it to cease to operate.

On the other hand, imagine a lake: it also have many diverse parts, also connected to each other, and also operating in tandem as part of an ecological environment, but some of its parts can be removed without shutting down its functions, even if its ecology changes.

A watch is a complicated system, while a lake is a complex system. Our discussion here is far from a purely academic one.

Complexity matters for understanding complex systems because they require particular problem-solving approaches. Our understanding of problem-solving approaches to complex systems might benefit from first examining the characteristics of more traditional problem sets and problem-solving approaches to them.

Problem solving is all about optimization, by which we mean finding the optimum solution to a problem. We might understand problems in the first type of problem set by thinking about them as “Mt. Fuji” problems. Mt. Fuji problems are those for which we can find one optimum solution. Take, for example, the problem of figuring out how many rounds of bullets we should issue police academy cadets to teach them how to shoot properly.

We might do this by issuing them a certain number of rounds for practice and then seeing how many can pass the requisite qualification test. Lets say we start with 50 rounds for practice and we find that 25% of the cadets pass the test. Then we give a new group of cadets 75 rounds and we find that 50% pass. 75% pass at 100 rounds, 85% pass at 125 rounds, and then 95% pass at 150 rounds. At 175 rounds we find again that only 85% are passing, and when we increase it further to 200 rounds the passage rate falls back down to 75%. Clearly we would want to do some more investigation into the reasons behind the decline, but suffice it to say that we reached our peak passage rate at 150 rounds. The point here is that in our example, we have one optimum solution to our problem.

Other problems look less like a simple line moving up towards a point and then declining and instead look more like a series of several periods of optimization surrounded by periods of lower optimization, which we might refer to as “Appalachian Mountains” problems. In such rugged problem landscapes, we might find that peaks in optimization are more localized than universal, and so to venture from one peak to another may require moving through a drop in optimization.

Take for example deciding which software program to use for geospatial analysis – something with which we should all be relatively familiar at this point. We might start out using Google Earth because it is a very common program and uses an intuitive user interface. It works great for some tasks, but over time we realize we need to be able to access the program even when we have no active internet connection and the type of analysis we are conducting requires more security than that available on the free version. So, we convince our boss to purchase a Google Earth enterprise license, and have now invested a little more to achieve a more optimum solution to the problem set of conducting geospatial analysis.

After a while, though, we find that Google Earth as a platform simply does not support the kinds of robust geospatial analysis we need. In order to conduct more advance analysis, we have to abandon Google Earth for ArcGIS, a substantially more expensive piece of software. In the short term we are actually electing to decrease the return on our investment for the promise of reaching higher optimization for our solution. But we (and our boss) decide it is worth the loss of the Google Earth Enterprise license we paid for (not to mention the loss in time required to learn a new program with a less user friendly interface) in order to acquire the advantages of ArcGIS. Later we find that with ArcGIS we need to purchase an extension that allows us to conduct network analysis – more investment, but with a higher return.

Over time, however, we find once again that we need an even more robust geospatial analysis program, like ERDAS Imagine that allows us to produce 3D cross-sectional renderings from large imagery datasets. So once again we have to assess whether it is worth it to accept a short-term loss in exchange for higher optimization.

While these problems may complicate our analysis, requiring us to increase our computations of payoffs and probabilities, traditional rational analysis still applies because the landscape itself is relatively stable. The rational analysis we traditionally use is often called decision theory, in which we determine our options, we identify the payoffs of each option, we compute the probabilities of success for each option, and then we make a rational choice to select the option with the highest payoff and chances of success at the lowest cost.

Meaning, once we have figured out the texture of the problem, we can determine what moves make sense even though they may require a temporary allocation of resources away from exploiting peaks in optimization and exploring the details of the landscape. This tension represents the tension present in any organization attempting to balance research and development and profitability derived from execution.

Complex problems, however, are a different beast entirely. They are neither Mt. Fuji nor Appalachian Mountains problem landscapes because the interdependence of their diverse, connected parts means that when one actor behaves in a certain way, the entire landscape shifts, re-distributing the presence of peaks and troughs in adaptive ways that cannot be determined beforehand.

We refer to the landscape of complex problems as ‘dancing landscapes’ because the connectedness and interdependence of their parts mean they are susceptible to the large-scale events that produce bottom-up emergent phenomena. Lets use al-Qaeda as an example of a complex problem. Members of al-Qaeda control almost nothing within the organization in themselves, even at the leadership levels: Lines of direct communication are diffused into layers of interpretive pathways.

Groups are often geographically isolated and more responsive to local conditions that the conditions of the organization as a whole. And yet, a single cell’s impetuousness, poor timing, or lack of caution can re-write the security environment in which the rest of the organization must operate. It is true that behaviors within local cells of al-Qaeda produce macro-level patterns that we might be able to identify as they emerge.

Because al-Qaeda is a complex social network, however, these larger patterns cause the local cells in turn to adapt, creating new patterns and undermining our ability to establish static representations of the organization. This characteristic of small movements in the system building toward massive shifts in the entire landscape leads us to one of the key problems with analyzing complex problems: they are non-linear.

Related to the concept of emergence, the second aspect we need to address in complex systems is that of their unpredictability. Unpredictability is merely the product of emergence, which simply occurs because a complex system is more than the sum of its parts. We can understand the behavior of emergence in a simplified way by thinking of three shapes: a triangle made of nine smaller triangles, a triangle made of nine smaller circles, and a circle made of nine smaller circles.

The triangularity and the circularity of the larger shapes are not dependent upon the presence of triangularity or circularity of the smaller shapes that compose them. Emergence produces the large-scale events that take place when elements in a system interact toward a tipping point where small adjustments build toward an overwhelming, unanticipated effect.

We might understand tipping points as the place in the system where one or more of its key characteristics (diversity, connectedness, interdependence, or adaptation) have either increased too high or decreased too low. The adaptive characteristic of complex systems notoriously masks signs of a major problem until it is too late. All seems well until suddenly and all at once, the system reaches a tipping point where everything exponentially changes in a way that could not have been predicted.

Given the aspects of nonlinearity and unpredictability that mean al-Qaeda does not operate through static optimization and produces large-scale, emergent events, what must our analysis of it as an organization include?

First, we must develop methods for weighing diversity within al-Qaeda as a system. Al-Qaeda sought to promote diversity within its organization, but with too much diversity it risked loosing its coherence (Abuza, 2003). To survive, al-Qaeda had to seek a balance between ineffective simplicity and ineffective chaos. We should come to recognize when processes are mobilized to establish that balance or when the organization suffers from the decay of groupthink.

Second, we must monitor what phenomenon incentives in the system actually produce. The adaptive characteristic of complex systems cause them to experiment mindlessly with every possible combination and promote the selection of those that actually work, regardless of how well they work according to an organization’s dominant logic. Al-Qaeda invested heavily in Iraq with the hope that successes there might promote its claim as the defender of the Islamic world against Western imperialism (Nasir, 2007). That investment, however, resulted in the emergence of Abu Musa’b al-Zarqawi whose uncontainable anti-Shi’a position forever concluded al-Qaeda’s ability to partner with non-Sunni sects of Islam.

Finally, we must identify opportunities for al-Qaeda’s improving its operations, but not in the way one might think. Destructive cascade effects can occur if al-Qaeda attempts to over-optimize its performance and lose the robustness provided by self-organized adaptability. Because its organizational mechanisms will respond reflexively to those threats, we may be able to determine internal threats before its members do themselves. While other approaches also merit exploring, these serve as a strong start down a long road of recovering our analytical capacity regarding the organization we have labeled our chief enemy for more than a decade.

Al-Qaeda, like other complex problems, is not a simple system that we can understand without accounting for key elements of its complexity and their interactions, although from the bulk of analysis about the organization, one would never know it. Though we continually act as though we can gain enough information about al-Qaeda to control it, we might be better off turning our resources towards attempting to harness it.

The rational decision-making model does not account for the behavior of other actors in the system - even though game theory has attempted to address this shortcoming. Classic decision theory translates complexity into uncertainty, orients action around capitalizing on knowledge rather than increasing it, and focuses on discrete outcomes.

Complex systems do not behave in ways that make these approaches useful. To understand al-Qaeda, let alone to act against it effectively, we must engage new mechanisms of analysis that account for the reality of al-Qaeda rather than the version of it that we would be most comfortable understanding.

Plenty of systems exhibit the characteristics of nonlinearity or unpredictability without being qualified by the kind of complexity we find when the two appear together. We may know that the weight of a rock is its radius cubed, for instance, so that if we double its size, its weight increases eight-fold, demonstrating nonlinear predictability. On the other hand, the quality of certain wines has often been found to have a linear relationship with the average temperature of certain months in the regions where the grapes for the wines are grown.

Since we cannot tell in advance exactly what the average temperatures will be, we have an example of linearity without predictability. As Heuer and Pherson discuss in Chapter 11 (2011), the intelligence community has generally taken four approaches to complex systems.

The first manages future unpredictability by establishing scenarios and indicators that enable analysts to track which of several possibilities appear to be emerging over the horizon.

The second involves the use of computer models and simulations. This approach used to be prohibitively costly in the past because it required the development of proprietary software or robust defense contracts to create the baseline models. With advances in the computer sciences, software programs like Netlogo provide analysts with substantially better access to the advantages of computer-assisted data analysis of complex systems.

Third, intelligence analysts attempt to predict the future based on their best guesses, not always adequately informed by expert judgment. Obviously this approach greatly increases the chances of an intelligence failure due to complex systems’ nonlinearity and unpredictability. Lastly, Heuer and Pherson introduce us to the Complexity Manager as a structured analytic technique.

Social Network Analysis

Social networks are one of the types of complex systems with which we are most familiar from our everyday lives, although we probably rarely think about them consciously. Social network analysis is a technique for understanding the influences of relationships between actors on the movement of resources within them. Social network analysis emerged from the fields of sociology and cultural anthropology (Prell, 2012), and has been heavily adapted for the field of intelligence analysis.

Its emphasis on the movement of resources is a key advantage in its use as a model for intelligence analysis because it can be used to track the movement of tangible goods and services, as well as intangible information and ideas. By understanding how the actors in a network interact, we can identify who controls the flow of resources, who is central to the network’s ability to operate, who links different parts of the network, and so on.

Your textbook reading for this week provides a fairly good introduction to social network analysis. This portion of the lecture supplements that information with some of the more technical aspects. In the Lessons menu for this week you will find an introductory text to social network methods by Hanneman and Riddle (2005) that you may find useful in your own work.

Behind a social network lies a binary matrix indicating the presence connections between actors. If one actor knows another actor, then a ‘1’ appears in the cell where they meet in the matrix, otherwise a ‘0’ appears. In Table 1 we see two types of matrices showing two types of relationship matrices. Asymmetric matrices show the direction of relationships when they are uneven. They might be used, for example, to show that one actor contacts another but the ability to contact does not go both ways. You can see in Table 1 that Marc has a relationship with Xu because there is a ‘1’ where he meets Xu in the matrix. But Xu does not have a relationship (of the same type being recorded, in any case) with Marc because there is a ‘0’ where he meets Marc in the matrix. Symmetric matrices are used to show raw connections without showing the direction of that relationship, either because a one-way relationship does not exist in the network or because the social network analysis was not constructed do conduct that kind of analysis.

The matrices used in social network analysis are often translated into visual graphs using two primary elements: nodes and ties.

In Figure 4 we can see a social network diagram of the relationships between a people in a group produced by a program called Netdraw, which is packaged with another common program used for social network analysis in the social sciences called UCINet (version 6.1 in this case). Each node is labeled – with the name of each person, in this case – and has lines connecting it to other nodes in the network. When we look at the lines themselves we see that they are directional, meaning that behind this diagram is an asymmetric matrix.

This graph also uses the symbology of the nodes to increase the amount of information communicated by varying the nodes’ shape, size, and color according to attributes we stored behind the data. Shape is used to show a person’s role in the organization, whereby a circle represents an instructor and a square represents a student. Color is used to represent gender, whereby red represents a woman and blue represents a man. Finally, size represents a measure of power in the network called betweenness, which we will discuss in detail next.

Measures of Centrality

As we mentioned before, we use social networks to track how resources move between nodes across the ties between nodes. One of the ways we understand this resource management is through measures of centrality, which offer insight into the relative power each node has within the network. Measures of centrality are quantitative values, meaning that they depend on algorithms to count the relationships between nodes represented by the ties – or, if we think in terms of the underlying matrices, they use matrix algebra to weight the ‘1’s against the ‘0’s. We can think of each tie as a pathway through which resources travel, constrained or propelled by the structure of the network.

How we process those pathways depends on how we define power, and we are usually interested in defining power several different ways when we conduct our analysis. Though we have many ways to think about power, we are going to cover three definitions in this lecture: degree, betweenness, and eigenvector.

Degree is probably the easiest for us to understand. The level of degree someone has in a network determines how many options they have. In visual terms, think of degree as being number of ties extending from a node to other nodes. In mathematical terms, degree is calculated by counting each node’s ties (or the ‘1’s in a matrix) and by ranking the values for each node. Under this idea of power, someone with high degree has the ability to access more people in the network than others, hence the number of options they have for accessing resources.

This may (and we say ‘may’ because it really depends on what we are looking for in a network) mean that a person has more autonomy in the network and is less dependent on others, making them more powerful than others with fewer options, a.k.a., lower degree. When using directional data we can distinguish between in degree and out degree. A high level of in degree indicates a higher power to receive resources, while a higher level of out degree indicates a higher power to disseminate resources.

Betweenness is a measure of how many times a node must be crossed when resources move from one part of the network to another. Many networks contain clusters of relationships, which we call cliques, where several nodes have many connections to each other. Between clusters we have what we call gatekeepers, which connect one cluster to another.

Gatekeepers have high betweenness because we keep running into them when we count all the different ways we can move from each node to every other node. In fact, running these permutations is exactly what social networking software does for us simply because in a very large network it is usually impossible or infeasible for use to calculate betweenness by hand. Based on their ability to control the communication or transmission of resources between clusters, gatekeepers may be considered powerful members of the network.

The last measure of centrality that we will discuss here is called eigenvector. With degree, we might think of power as the number of people a person knows. But with eigenvector, we might think of power as the number of people another people knows who knows other people. For example, lets say we have are examining Person A and Person B. Person A is directly tied to 100 people, and each of those people are tied to 1 other person. Person B is directly tied to 10 people, but each of those people are tied to 100 other people. Person A has the highest degree because she can access 100 people, whereas Person B has the lowest degree because he can only access 10 people. However, Person B has the highest eigenvector because he can access 1,000 people within only one step, while Person A has the lowest eigenvector because she can only access 200 people in one step. We might say that Person A “knows people”, while Person B “knows people who know people”.

Does that mean Person B is more powerful than Person A? Well, that depends on what we are looking for in the network and how we define power for the purposes of our analysis. In this example we calculated eigenvector by only considered one step, but the measure of eigenvector is actually calculated by looking at all steps within the network. For this reason, eigenvector is one of the hardest measures of centrality for us to identify purely by visually inspecting the network. Large networks demand we use social network analysis software to the ‘heavy lifting’ for us. Similar to degree, we can use directional data to track out eigenvector and in eigenvector.

Figure 5 shows us the calculations for in degree, out degree, in eigenvector, out eigenvector, and betweenness for the network shown in Figure 4. If we wanted to analyze relative power within this network, out degree and out eigenvector would not be particularly helpful because everyone has the same measure (0.176 and 4.243, respectively). Based on in degree, Pam and Steve have the lot of power. Based on in eigenvector, Pam has a relatively high measure of power. And based on betweenness, Holly has a high measure of power. Who is the most powerful person in the network? Again, it depends on what we are looking for.

That being said, if we were considering power within the network as a whole based on just this information, then we would probably put our money on Pam because she shows up twice (and once in an extremely high position). Of course, there are many other measures of centrality that we may want to calculate and examine before we labeled any one person as the most powerful, and even then we would not be able to establish that person’s criticality within the network without including functionality in our analysis.

Functionality and Criticality

If centrality serves as the quantitative measure of power in a network, then functionality serves as the qualitative measure of power. In fact, calling it a ‘measure’ is already misleading because there are no calculations for functionality that we can call upon to automate this aspect of our analysis. Functionality is heavily dictated by the data we are using to draw ties between nodes, and it often requires a certain level of cultural expertise to interpret.

For example, lets say in a network we have a man connected to a woman who is his wife, and connected to another man who is his brother. In our culture, a tie between a husband and wife means something specific about their relationship and sharing of resources: she is by default his next of kin, his legal medical proxy, the inheritor of his wealth after his death, and the custodian of their children.

In some cultures, that relationship exists not between a husband and wife, but between a man and his brother, and especially so if his brother is his older brother. Ties between nodes alone do not represent this aspect of social network analysis, but we must account for it if we are to determine a person’s criticality within the network.

When we combine centrality and functionality, we can determine centrality. Centrality refers to a person’s overall importance, both in terms of different quantitative definitions of power and different qualitative assessments as to the nature of relationships within the network. By understanding a person’s criticality, we can begin to draw some predictions about how the network will behave if a person is removed or if a person’s status changes.

Without criticality, we have few means to prioritizing our targeting in the event that we want to destroy, disrupt, or perhaps even coopt (remember our discussion about complex systems and the advantages of harnessing them over attempting to control them) the network.

References

Abuza, Z. (2003). Militant Islam in southeast Asia: Crucible of terror. Boulder, CO: Lynne Rienner Publishers.

Hanneman, R.A., Riddle, M. (2005). Introduction to social network methods. Riverside, CA: University of California-Riverside.

Heuer, R.J., & Pherson, R.H. (2011). Structured analytic techniques for intelligence analysis. Washington, DC: CQ Press.

Mitchell, M. (2009). Complexity: A guided tour. New York, NY: Oxford University Press.

Nasr, V. (2007). The Shia revival: How conflicts within Islam will shape the future. New York, NY: W.W. Norton & Company.

Prell, C. (2012). Social network analysis: History, theory & methodology. Thousand Oaks, CA: Sage Press.

All the Key Players

On Day 7 of last week you presented your argument to the Tucson JTTF explaining your progress in your case against El Movi and the process you used to achieve your results. You had a chance to review their positions, as well, and after some conferencing mediated by SA Franks, the SAC of the JTTF has directed the DEA and the FBI to refrain from interfering with your operation with the promise that when the case reaches a point where the TPD are ready to bring down El Movi, you will have the JTTF’s full support. Not a bad deal, all things considered, but your work is not over, yet.

Situation

Encouraged by your success, Chief Heaton decides to confide in you that during Week 3 when Daisy made her connection to El Movi known, the Chief, in coordination with the Tucson District Attorney’s office, secured wire taps on the telephones of the brothel managers who had been contacting Daisy for the their weekly grocery deliveries. The work you had done was sufficient to acquire the wire tapping warrant, and now he would like you to conduct your ‘magic’ on the resulting SIGINT information. You have been able to process the SIGINT into a representation of El Movi’s communications network that you will use to interpret measures of centrality of the network’s members. You have also been able to review the transcripts of the conversations in order to glean some information about the functionality of those relationships, which will help you identify critical nodes in the network.

From what you have discerned, the network is composed of 17 active brothels, although the number was 18 until Julia and Marco’s brothel was shut down in Week 1 (closely resembling the information you originally received from Daisy). A man referred to only as Angél remains the leader of El Movi. He actively directs the network’s activities but stays away from the actual brothels themselves. He appears to use the brothels as his own source of income, with no identifiable connection to other organizations. If anything, Angél might be accused of micro managing, but he does not speak to the brothel managers aggressively, indicating a high level of cooperation within the network.

Each brothel has one man and one woman who manage it. Angél prefers having a man and woman working together because the men manage the brothels’ security and the women manage the brothels’ victims. Only the men seem to use their ‘work phones’ to communicate with other members of the network, perhaps as a security measure. When the men managers talk about the women managers, the women are always referred to as “busy”, but you cannot tell what that means since they all seem to understand its meaning implicitly. The men brothel managers are in constant communication with each other in order to maximize their ability to transmit information between them efficiently.

Based on their conversations, you gather that within half an hour of the police showing up at Maria and Marco’s brothel back in Week 1, every other member of the organization had been informed about it. For his part, Angél seems to use their relationships to keep tabs on his ‘employees’, with the idea probably being that if one tries to cheat the organization or become a police informant, the organization will find out about it sooner rather than later, at least this is how the brother managers interpret it.

Six of the brothel managers serve as Angél’s deputies. Four of the managers – referred to only as Adam, Garrett, Sid, and Chris – travel around to all the brothels once a month to collect money, all in cash, and deliver it to Angél himself. Two of the managers – referred to only as Jesse and Mike – are in charge of meeting the trucks used to transport victims to the brothels. You suspect these two are in contact with their Mexican counterparts to arrange for the “deliveries”, but the warrant for wire-tapping does not appear to cover whatever means of communication they are using.

While none of the brothel managers seem to be of low intelligence, Angél’s deputies seem particularly articulate. You wonder if maybe Angél recruits his managers specifically because they are not the type of people you would suspect might be running a human trafficking ring if they were your neighbors.

To validate whether what you are seeing in the functionality of these relationships translates into these individuals criticality within the network, you will need to include in your analysis as assessment of their centrality. The communication network as a whole consists of 293 nodes – way too many for you to analyze without narrowing them down. Most of the nodes seem to represent casual connections not directly involved in El Movi but bumping into their communications network by coincidence: plumbers, telemarketers, local pharmacies – all the common phone calls you would expect to see but that have nothing to do with your investigation.

After dropping all the outlying nodes, you have substantially fewer nodes to analyze. Further examination indicates most of these are clients of the brothels or other facilitators of the business. While of interest, these may not be as useful for bringing the network down as a whole, and the District Attorney has already made it quite clear to you that she has no intention of pursuing prosecution against all those people. So, you have to prioritize where you want to focus your efforts. Because directionality is not important at this stage, you only focus on degree, eigenvector, and betweenness. And this is what you have found: