Chapter 7

Conceptualizing the Problem

Bottom Line Up Front

Critical thinking requires the conceptualization of the problem by identifying and defining concepts, employing theories and models, and generating hypotheses. It starts with conceptualizing terms that allow people to think more clearly and share their thoughts with others. Conceptual theories may already exist or may be created by modeling, which combines facts, assumptions, logic, and reasoning to help people understand a situation. Hypotheses are simply statements of relationships between various components of a theory or model. The hypotheses are tested with empirical data to determine if they support the theory. This chapter describes categories of models used regularly in security analysis. Most analytic projects require a number of different models to fully understand the research topic.

Concepts Allow Thinking

People inherently use concepts in their daily lives. Concepts are intellectual constructs that enable people to identify, organize, interpret, and compare ideas resulting from their experiences and thought processes.¹ Concepts lead to words and symbols, which—when combined with grammar—create languages. Grammar provides the rules for using words and symbols. Clearly people think and share their thoughts using language, but the constructs of language vary by the people who use them and the environment where they live. For example, the English language has only a few words for “snow,” but Native Americans living in the Artic have over 50 words in their languages for different types of snow. These many words for snow developed to provide specific descriptors of their harsh living environment.²

Defining words and symbols is an important part of language. Definitions allow the conceptualizing of ideas or thoughts, especially in creating a generalized idea of a thing or class of things. Agreed-upon definitions lead to clarity among people using the same language. Defining concepts usually includes designating the concept, identifying dimensions of the concept, and agreeing to indicators or attributes of the concept. In social science, the indicators and attributes lead to development of operational definitions of a concept, such that the concept may be measured and used to test hypotheses or otherwise employed in analysis (Chapter 3). Figure 7.1 provides a diagram defining the economic dimension of the concept of Marxist Socialism.

Figure 7.1 highlights the complexities of defining concepts. To operationalize (or measure) the Marxist Socialism concept, the analyst could determine the percentage of state ownership of production, percentage of production facilities managed by workers, and/or the distribution of benefits from the production activities. There may be different or competing definitions for general concepts. For example, the more general term “socialism” has several conflicting definitions used by those seeking to support their arguments. Marxist Socialism is the normative idea of 19^th-century German philosopher Karl Marx (see Appendix III for a more detailed discussion of Marxism). There is no evidence that Marxist Socialism has existed anywhere in the world at the state level. Authoritarian Socialism, as deployed in the Soviet Union and other authoritarian states, does entail state ownership of production; but, authoritarian elites—not the workers—manage and primarily benefit from that production. Democratic Socialism, as enacted in many modern democratic states, entails private ownership and management of production; however, it stresses that workers equally benefit from production, including providing an economic structure of socially-just capitalism and robust social welfare programs. (A better designation for this concept is Social Democracy.) In political discourse, these three versions of “socialism” have been used interchangeably depending on the speaker’s or writer’s agenda. This can lead to an equivocation logic fallacy (Appendix I), where definitions of concepts change based on the situation. This usually leads to speakers or writers “talking past each other” as they employ different conceptual definitions that can result in decreased clarity in the exchange of ideas.

Each state and organization has its own concepts. Some will be general concepts used in the larger society, while other concepts will be specific to the state or organization. (Try understanding a Pentagon conversation where every other word seems to be an acronym!) Achieving clarity in the use of concepts often is challenging. Most concepts exist unconsciously in vocabularies and belief systems. Concepts often only surface in a person’s speech, writing, or behavior. Similar to assumptions and beliefs (Chapter 6), concepts reside in supporting clusters. For example, before a person can understand the concept of “ethics,” he/she also must understand concepts such as justice, fairness, kindness, cruelty, rights, and obligations.³ Security analysts employ models to assist in understanding the complexity of concepts.

Modeling

Security analysts employ modeling to expand individual concepts by combining known facts, assumptions, logic, and reasoning to assist them in conceptualizing a situation. Once a model is created, populating it with historical or current facts helps the analyst generate findings from their analysis (Chapter 9). Modeling also may assist in uncovering assumptions (Chapter 6) and developing alternatives (Chapter 8), in addition to identifying problems with logic and reasoning, which might otherwise go unnoticed. Modeling can create theories, and both models and theories generate hypotheses to be tested or to generate other insights that can lead to a better understanding of a particular situation. Overall, modeling can improve the rigor and precision of security analysis. When models are presented to security customers, one objective is to ensure customers are not confused as to whether they are seeing facts, assumptions, or hypotheses.⁴ This chapter provides a summary of the most frequently used models in security analysis. For more robust coverage of security analysis modeling, see Robert M. Clark’s Intelligence Analysis, A Target Centric Approach⁵ and Richard L. Kugler’s Policy Analysis in National Security Affairs: New Methods for a New Era.6

Models provide a representation of an object, idea, or system. That is, when analysts cannot interact directly with the object, idea, or system; models can provide insights to improve understanding.⁷ Figure 7.2 provides Clark’s hierarchy of models that inform the remainder of this chapter.⁸

Physical models represent tangible items; that is, something a person can touch.⁹ They are descriptive and used to answer questions of who, what, when, where, and how. Physical models include maps, globes, pictures, clocks, calendars, organizational charts, equipment plans, building plans, and many more physical items. Scale models of ships, aircraft, spacecraft, etc., also are included in this category.

Conceptual models are constructs of the mind and are generated by a person’s ideas and thoughts. These models often are displayed on paper or in other mediums and may lead to the construction of physical models. Conceptual models often are abstract models; that is, they do not necessarily reflect reality, but they still are useful because they provide insights to improve understanding. Abstract models often simplify reality, allowing people to better understand highly complex situations. For example, the abstract model of “left-brain or right- brain thinkers” is decades old. This model offers that the left-brain is where facts reside and are organized, then combine with logic and reasoning to facilitate thinking. Left-brain thinkers are considered analytic. The right-brain is where imagination, artistic abilities, etc., reside. Right-brain thinkers are considered creative. Today, with the improved technology of brain scans, it has been found there is no left or right brain at work as the abstract model offers. Instead, there are different parts of the brain active when a person is being analytic and other parts when the person is being creative. Thus, while this abstract model does not reflect reality, it does provide a model for understanding how different cognition tasks energize different areas of the thinker’s brain. It is still used today to indicate analytic (left-brain) and creative (right-brain) thinkers.

Conceptual models also may be characterized as either normative or descriptive. Normative conceptual models describe what “should” or “ought” to be. They do not present reality; but, instead, provide insights on how to understand or improve on reality. Normative models can be used to develop a best or preferable alternative in a situation.¹⁰ Agency models, especially decision- support models addressed later in this chapter, are usually normative conceptual models. Security analysts—both academic and practitioner—spend considerable time developing descriptive conceptual models to answer who, what, when, where, and how. These models also address why a situation happened (an explanatory study) or what will happen in the future (a predictive study).

Descriptive conceptual models range from the less to the more complex as displayed in Figure 7.2. These models have one or more of the following traits:¹¹ Deterministic versus Stochastic. Deterministic models display exact relationships among factors or variables. As a result, there is little uncertainty surrounding the outcomes of deterministic models. For example, centuries of solar observations, combined with the ability to mathematically calculate the time of sunrise and sunset, allow people to know exactly when the sun will rise and set each day. This is a deterministic model. There are few, if any, fully deterministic situations (i.e., near 100%) in social science. Stochastic models are based on probabilities. While the relationships of factors in stochastic models are often not known specifically, trends may be determined and probabilities estimated for the relationships. Because of human “free will,” most models of human behavior, decisions, and conditions are stochastic. Because analytic findings seldom receive 100% confidence levels, social science inference views the world as probabilistic, as it will always have a chance of being wrong.

Linear versus Nonlinear. Linear models indicate a sequential, consecutive, step-by-step process or other display of factor relationships. The Security Analysis Critical-Thinking Framework model displayed at the start of this chapter could be considered a linear process if the analyst only addressed one step or element after another in the order shown. In fact, the process is not linear and is more complex, as the analyst will revisit each element several times during an analysis. Simple linear models are often based on the mathematical formula for a line, where on an X-Y graph:

Y = mX + b

Y = dependent variable

X = independent variable m = slope of the line

b = where the line crosses (intercepts) the Y axis.

Correlation analysis graphs (see Figure 7.3) and some statistical regression models assume linearity in relationships and are based on the mathematical formula for a line. Nonlinear models depict highly complex relationships that cannot be modeled as linear. Some models of economic relationships are highly complex and may not be based on linear relationships. To simplify complexity, economic analysts may employ statistical econometric models, assuming relationships are linear.

Static versus Dynamic. Static models are snapshots in time that capture relationships within a limited time period and assume the model’s prescribed components remain unchanged for that time period. Static models are often linear. An example is a spreadsheet that records data on relationships for only a limited time period. Structural and functional models are usually static, but also could be dynamic. What static models often ignore is how the model’s relationships often do not reveal the synergistic effects of how the combination of the components may be enhanced as they work together over time. Dynamic models include relationships over several time periods. A dynamic model is iterative, as it constantly updates the effects of relationships over the selected longer time period. Process models (covered in more detail later in this chapter) usually are dynamic because they depict the flows of people, materials, and behaviors over time, in addition to often showing feedback as the process proceeds.

Solvable versus Simulated. Solvable models are those where an answer can be determined. This usually means that a causal model demonstrates changes to a dependent variable, or a process model that results in an output. For example, mathematical and statistical models usually are solvable. Simulated models are used for situations that are so complex that related mathematical or statistical models cannot be designed or solved to capture the complexity. Simulated models often can be solved through either computer simulations or physical “table-top games,” where using a “what-if” approach a model’s component activities can be simulated and the resulting consequences assessed. This includes simulations taking place over a longer period of time, such as the movement of forces in a naval war game over a period of weeks or months.

Basic Models

Models can take on different forms depending on the situation under study and the research questions being investigated. These include basic models, including list models, graphical models, matrix models, organizational models, linkage models, and flowchart models. Following sections describe geospatial models, temporal models, process models, structural causal models, and agency models in more detail. Most analytic projects employ a number of differently formatted models to capture the relationships and provide insights on the situation under study. Analysts often will use comparative models to generate competing alternatives and then compare results. For example, one U.S. and one foreign hypersonic missile system may be modeled and compared to determine which is superior; and, if the U.S. system is not superior, to assist in its improvement.

List models are the simplest models and frequently are used on a wide range of topics such as lists, checklists, and outlines. Figure 4.3 is a checklist model analysts may use for starting a research project. Figure 6.3 is a list model of items to investigate in developing a psychobiography of a world leader. This book’s Table of Contents is an outline model of the book’s contents. A popular list model is the pros-cons-fixes model, which is discussed in Chapter 9. This model allows the analyst to assess and compare the pros and cons of several alternatives, while also investigating fixes to the cons. Many of the analytic techniques presented in this book are list models.

Graphical models summarize and display large amounts of information and demonstrate relationships in easily understandable formats. Column, line, pie, bar, and area charts frequently are used as graphical models in security analysis. Scatter plots are also a widely used option. Customers of security analysis products are familiar with these graphical models as they see them often in the news media, literature, and briefings. Computer word-processing, spreadsheet, and presentation software programs allow the easy creation of graphical models.

Figure 7.3 is an example of a scatter plot of economic freedom and corruption in selected world states. The economic freedom data is from the Heritage Foundation’s 2020 “Index of Economic Freedom” and is measured on a scale of 0-100, where higher values indicate more economic freedom.¹² The corruption data is from the Transparency International’s 2020 “Corruption Perceptions Index,” also measured on a scale of 0-100, where higher values mean less corruption.¹³ The Pearson’s r (correlation coefficient) for Figure 7.3 reveals a +.78 value, or a strong positive relationship between the selected state’s index ratings on economic freedom and corruption. A visual evaluation of the data point distribution, confirmed by the dotted trend line on the scatter plot, also indicates a positive correlation between increasing economic freedom and decreasing corruption. In evaluating this scatter plot, keep in mind that “correlation does not mean causation,” so the analyst must develop or find a theory supporting a causal relationship between the two variables. In the case of this scatter plot, Appendix III offers a Theory of Political Culture that establishes a relationship of how more economic freedom correlates with lower corruption levels in world states. See Appendix III for more details on this relationship.

Matrix models organize information in tables of columns and rows that may include assessment factors, alternatives, data, and/or evaluations, which allow the analyst to view relationships and make inferences. These models are flexible and frequently are used in security analysis. Appendix III, Figure III.1 is a complex matrix model of a Theory of Political Culture. Chapters 9 and 10 provide additional discussion on creating and employing matrix models.

Organizational models are descriptive models that reveal the key personnel and components of a government or other organization. Before beginning a psychobiography (Chapter 6), the analyst should first develop an organizational model to capture the key personnel to be investigated. Figure 7.4 outlines the key personnel and groups in the 1980s’ Pablo Escobar cocaine smuggling organization. As discussed in later sections, Figure 7.4 can be a starting point for analyzing and targeting that cocaine smuggling organization.

Linkage models are relationship models that show the relationships between key personnel in a particular situation. Figure 7.5 demonstrates the key relationships and some biographic information of the leaders of the Medellin cocaine cartel during the 1980s. While the Pablo Escobar organization (Figure 7.4) was at the center of the cartel structure, Escobar allied under the Medellin Cartel umbrella with other traffickers specializing in the transportation and distribution of cocaine. Some of the cartel members surrendered to the Colombian government in the early-1990s after the government offered reduced prison sentences to those who voluntarily turned themselves in to government officials. Law enforcement makes wide use of linkage models during its investigations; for example, when they link suspects and persons of interest to telephone numbers, addresses, bank accounts, identifying documents such as driver’s licenses, passports, vehicle registrations, and any additional information pertaining to the investigation.

Flowchart models are used extensively in management, intelligence analysis, and policy analysis. Management specialists use flowcharts to depict business and government processes that can lead to improved outputs. In intelligence analysis, flowcharts help analysts define and better understand the targets. In security policy analysis, flowcharts help analysts design and improve programs. Figure 7.6 demonstrates the process for developing and deploying counter-narcotics military or law enforcement units. Many of the models in the following process-modeling section, especially in system and network analysis, make use of flowcharting techniques.

Geospatial and Temporal Models

Security analysts make wide use of geospatial and temporal models. Geospatial models take place in space—meaning with building plans, terrestrial maps, celestial maps, globes, and other descriptive models. Temporal models capture the concept of time (minutes, days, weeks, months, or years) as it relates to the situation under analysis. When used together, geospatial and temporal models often are powerful for providing customers with visual representations of a situation.

Geospatial Models. Relying heavily on maps and imagery, geospatial models are readily understood by customers of security analysis who view maps and imagery in the news media, other literature, and on their personal Geographic Positioning Systems (GPS). Geospatial modeling has been around since the first maps were prepared centuries ago. By combining maps and/or imagery with other data, the displays may be used to visualize complex spatial relationships.¹⁴

Figure 7.7 is a map of Colombia showing the locations of coca growing areas and the locations of Revolutionary Armed Forces of Colombia, an insurgency group known as FARC that in the 1990s became involved in the growing of coca and production of cocaine.¹⁵ The map also shows Colombia’s maritime boundaries, international boundaries with other states, and the internal boundaries and names of Colombian departments. Depending on the research topic, other items could be included with the map of Colombia. This is an example of a common use of maps and other related data in intelligence analysis, policy analysis, or military planning and operations.

Military analysts often create geospatial models for planning and conducting operations. These are commonly known as human terrain maps. Using maps of their operating area, a Colombian military or police analyst planning an operation against insurgent groups or drug cartels in a localized area may create a human terrain map that describes the following potential targets of interest:

• The boundaries of each insurgent group and/or the drug cartel’s area of control, with specific attention to where areas adjoin or overlap.
• Identities and locations of insurgent group and drug cartel leaders, with photos and contact information (for monitoring), if available.
• Location and contact information for village, town, city, and federal officials.
• Locations of large farms/estates, churches, schools, and markets.
• Locations of public, private, and clandestine ports and airstrips.
• Patterns of activity such as movement into and out of the area, especially related to coca growing, cocaine production, and cocaine shipments.
• Nearest locations of Colombian military and police forces, including any private security groups.
• Economic driving forces in the area, including occupations and livelihood of inhabitants and employment and unemployment levels.
• Access to essential services such as fuel, water, medical care, and emergency services (fire, paramedics, etc.).
• Concerns and issues of the local population.¹⁶

Digital software programs are used widely in creating geospatial models. The software allows the merging of digital geographic maps, digital imagery, and database information to create visual displays security analysis customers easily understand. It is critical for security analysts to have access to and become proficient with these software programs.

Temporal Models. Time shapes events, so logically, timelines are critical to most events in security analysis. There are different techniques for temporal models, but here the focus is on simple timelines and basic time-series analytic models.

Simple timelines display events against time. The time periods (hours, days, weeks, months, or years) may be annotated on a map, poster board, bulletin board, or other suitable display. The corresponding events then are displayed near the time they occurred. Items to look for in simple timeline analyses include:

• Sequence—some events can only occur after others.
• Contingency—some events must be followed by others.
• Interval of time—some events must follow others at prescribed times.
• Time period—some events differ substantially from similar events in previous time periods.

Simple timelines often are combined with linkage models to show relationships between time, events, and people. Detective movies and television programs demonstrate simple timeline and linkage models. For example, when detectives begin investigation of a criminal case, they establish an evidence board (e.g., crime board, murder board, or crazy wall). Using a vertical display board where the detectives create a left-to-right timeline across the bottom or top of the evidence board. Adjacent to the timeline, they post pictures or descriptions of victims, suspects, persons of interest, or other persons on the periphery of the crime. Adjacent to each picture or description, the person’s profile is posted by marker, cards, or sheets of paper. The profiles include the person’s background information and alibi. Geospatial maps annotated with event locations, corresponding time lines, and other information may be included. The detectives also may post sticky notes or cards with additional information such as questions to be answered or alerts about gaps in the information. They then create a linkage model using strings or lines to show relationships among persons and/or pieces of information. They check information against the timeline to uncover inconsistencies. Their eventual goal is to find connections between the information and the timeline to identify the criminals. This same evidence board technique may be applied to a variety of security analyses.

Another frequently used timeline model are Gantt charts, which were invented by U.S. engineer Henry Gantt in the early 20^th Century as a project management tool. A Gantt chart is a useful way of showing activities or events displayed against time. On the left of the chart is a list of the activities and along the top or bottom is a corresponding time scale. Each activity is represented by a bar, where the position and length of the bar reflects the start time/date, duration, and end time/date of the activity. This allows the analyst or project manager to see at a glance:¹⁷

• What the various activities are.
• When each activity begins and ends.
• How long each activity lasted or is scheduled to last.
• Where activities overlap with other activities and by how much.
• The start and end dates of the entire project.

Figure 7.8 provides a Gantt chart for the construction of a new Russian aircraft carrier. In this example, the security customer questions how long it will take the Russians to build a new aircraft carrier and ready it for operations. The analyst constructs a Gantt chart from previous timeline data on Russian military shipbuilding. This example assumes all design work on the aircraft carrier is complete and the project has been approved and funded. The customer’s answer from Figure 7.8 is that it will take five years to build a new aircraft carrier and make it ready for operations.

Another common temporal-modeling technique is time-series analysis, which models events sequentially over time. This type of analysis has application to most social science fields. Basic time-series models are descriptive and provide insights from the data, where advanced time-series models may be used to establish causality among several variables measured over time or individual events organized by time. Time-series models often are used to make predictions. By plotting descriptive measures sequentially over time, an analyst can look for trends, seasonality, and cycles in the data. Trends in data include those that are positive (upward) trends, negative (downward) trends, or no detectable trends. Seasonality is when the data reveals predictable patterns recurring or repeating over regular intervals. Cycles occur when a series of data points follow an up-and- down pattern that is not seasonal. Cyclical variations in the data may include highs (peaks), lows (recessions), troughs (depressions), or expansion (increases).

The most basic time-series models are line diagrams that plot one or more variables over time. Table 7.9 provides a basic time-series model of four variable measurements: (1) 1990 to 2008 South American cocaine production, (2) cocaine interdiction in the America’s source and transit zones, (3) North American cocaine demand (1998-2008 data only—includes U.S., Mexico, Canada), and (4) U.S. cocaine consumption. The data for this model came from the United Nations Office on Drug and Crime World Drug Report 2010.¹⁸ This time-series chart reveals there is no seasonality or significant cycles in the data, but the trends in the data result in the following insights:

• Cocaine production minus source and transit-zone interdictions exceeded North American cocaine demand (fairly constant around 400 metric tons/year) for each year in the period 1990 to 2008. While the largest cocaine demand is from North America, this data does not include the demand in Europe or Asia, which must be supplied by the same cocaine production processes. Also not shown are arrival-zone cocaine interdictions in North America, which affects the availability of cocaine for sale.
• U.S. cocaine consumption trends gradually decreased from 1990 to 2008 from 447 metric tons in 1990 to 155 metric tons in 2008. Whether this decrease is related to increased U.S. supplies of other drugs (heroin, methamphetamines, fentanyl, prescription drugs, etc.) is an area for further research.
• Cocaine interdiction trends gradually increased from 1990 to 2003 and then increased more rapidly from 2002 to 2008. Why the interdiction trends increased from 2002 to 2008 is also an area for further research.
• The U.S. kingpin strategy to dismantle the leadership of the Medellin Cartel was completed by 1993, as depicted in Figure 7.5. Their rival Cali Cartel was dismantled by 1995. Disruption of the two largest Colombian cartels appears to have had little impact on cocaine production during the 1990s. This is another area for further research.

Advanced time-series analysis allows testing of causal relationships over time by employing advanced statistical techniques. Some statistical techniques can lead to causality findings or provide other insights with as few as 8-10 data points. To use the more powerful statistical techniques for time-series analysis usually requires evenly spaced data from approximately 50 time period data points. These advanced time-series statistical techniques require specialized instruction and statistical software and are beyond the scope of this chapter.

Process Models

Processes are presented as models and include steps and relationships that lead to an output. Process models may be conceptual-descriptive, as they attempt to capture what actually happens during a process. These models take the perspective of an external observer who looks at the way a process has been performed, allowing determination of the improvements that should be made to make it perform more effectively or efficiently. Process models also may be conceptual-normative; that is, defining the desired processes and how they should or ought to be performed. Normative process models also can establish rules, guidelines, and behavioral patterns, which, if followed, should lead to the desired output. Management specialists use process models to develop and improve business or government outputs. Intelligence analysts use process models to better understand the threat. Policy analysts use process models to design and improve programs to address threats or solve problems. Figure 7.6 could be used as a policy process model by analysts designing counter-narcotics troop deployment programs. Security analysts make most use of the system and network process models described below.

Systems Analysis. This type of analysis usually employs a number of models to demonstrate the linkages, interactions, and elements of a specific system. This may include models of political, economic, and/or social systems. Security analysis also may find a need to model infrastructure, information, communications, or weapons systems, among others. When creating a system model, Clark highlights the models should consider:

• A system has structure. It is comprised of parts that are directly or indirectly related. It has a defined boundary, physically, temporally, and spatially, though it can overlap with or be part of a larger system or network.

• A system has a function. It receives inputs from, and sends outputs into, an outside environment. It is autonomous in fulfilling its function. A ship is not a system. A ship with crew, fuel, ammunition, and a communications subsystem is a system.

• A system has a process that performs a function by transforming inputs to outputs.¹⁹

Most intelligence system target models have subordinate subsystems. The majority of intelligence target systems are complex systems because they are dynamic and evolving. They are usually nonlinear and often are not adequately described in simplified models. However, attempting to create simplified models of complex systems is a starting point for security analysis.²⁰

Figure 7.10 displays a system model for cocaine production. The function of this system is to produce cocaine hydrochloride, which can be sold on the illegal drug market. Each step in the cocaine production system is a subsystem, which could be displayed in its own more detailed diagram.

Figure 7.11 is an Ishikawa (fishbone) model that breaks down Figure 7.10 and its subsystems into key components as defined under the characteristics of Machines, Methods, Materials, Manpower, and Mother Nature.²¹ Ishikawa models are very flexible in displaying underlying factors that lead to process outputs. They also may be used for structural causal modeling (discussed below). Security analysts can use Figure 7.11 to develop intelligence collection and operational plans to target and disrupt the cocaine production system. While security analysis typically targets systems, it also allows development of operational plans to target key components of a system, such as the coca fields, cocaine labs, transport vehicles, precursor chemicals, etc., as shown in Figures 7.10 and 7.11.

Network Analysis. Most complex systems reside in networks, where a number of interrelated system models make up a network. Networks consist of nodes with links between them. The nodes can be any type of entity such as people, places, processes, things, or concepts.²² Social network analysis models are expanded link models. They entail identifying nodes (e.g., people) and their relationships (e.g., links) with other nodes (other people), including the number and types of interactions between nodes that indicate the strengths of the links. Figure 7.5 is the start of a social network model for the Medellin Cartel.

Security analysts usually create models of target networks. Intelligence analysts begin the target network development with a focus on the target threat. Policy analysts then use the target networks to devise plans to counter the threat. In the words of U.S. Army General Stanley McChrystal, former U.S. forces commander in Afghanistan, “It takes a network to defeat a network.”²³

Social network analysis helps identify the who in a situation. Target network analysis helps identify the what, when, where, how, and why of the situation. Network analysis helps determine the importance of individuals or organizations within networks and the resources or assets available to these individuals or organizations.²⁴

Figure 7.12 provides a network model of a cocaine cartel target.²⁵ It depicts the systems identified in Figure 7.10, Step 1 (coca supply) and Steps 2-4 (processing infrastructure). It adds systems for transportation and distribution infrastructure and leadership, which would include the Figure 7.5 leaders if the target was the 1980s Medellin cartel. Links for process flow and control are included in Figure 7.12. From this figure, the target network model would be developed by intelligence analysts as they sought to understand the structure of a cocaine cartel network threat.

Figure 7.13 overlays the Figure 7.12 target network with a disruption network of host-country and U.S. law enforcement and military forces.²⁶ The function of the disruption network is to prevent the cocaine target network from delivering cocaine hydrochloride to customers. Host-country law enforcement is designated for disrupting the target leadership and also the coca supply and processing infrastructure, as depicted in Figures 7.10 and 7.11. U.S. law enforcement and military forces are designated to disrupt the transportation and distribution infrastructure both in the transit zone (from host country to the United States) and arrival zone (inside the United States).

Figure 7.14 provides more detail to the U.S. disruption network as it existed in the 1990s. It displays the network designed by U.S. policy analysts and lists the major organizations and resources involved. Host-country law enforcement and military forces in the source (or production) zone normally require U.S. equipment, training, and intelligence support coordinated across several U.S. agencies by the U.S. State Department (DOS). Figure 7.6 depicts the process where the DOS would coordinate U.S. assistance in the host country to develop counter-narcotics units. In 1982, President Reagan declared illegal drugs a U.S. national security threat, leading to the evolution of the transit zone structure and increasing resourcing of the arrival zone structure shown in Figure 7.14. This included the support of the U.S. DOD and IC. DOD formed joint interagency task forces to direct and coordinate both DOD, U.S. Coast Guard, and allied air and sea forces in the maritime transit zone, along with U.S. law enforcement agency input and coordination. In the arrival zone, both along the U.S. coast and in the U.S. interior, the Office of the Director of National Drug Policy Control created interagency High-Intensity Drug Trafficking Area (HIDTA) offices to coordinate intelligence sharing and interdiction operations in designated U.S. geographic areas. The IC supported the disruption network strategy in the source, transit, and arrival zones. Each of the boxes in Figure 7.14 has its own networks, systems, and subsystems as part of the larger strategic network.

Figure 7.15 provides an example of the further decomposition of the international cooperation system in Figure 7.14. In the 1990s, U.S. international cooperation in the disruption of illegal cocaine smuggling came under the dual responsibility of DOS and DOD. Figure 7.15 depicts the assignment of responsibilities to each department. DOS coordinated host-country assistance programs, negotiated international counter-narcotics agreements, and engaged foreign country governments in both the source and transit zones. Through joint interagency task forces, DOD coordinated participation by allied (NATO, OAS, etc.) air and sea forces; hosted allied and host-country (source and transit zone) liaison officers at their headquarters; and engaged senior, foreign law enforcement and military officials in both the source and transit zones. As can be seen in Figures 7.14 and 7.15, U.S. participation in disrupting illegal drug smuggling is a highly complex, networked structure.

Structural Causal Models

Structural causal models are abstract and normally include a number of structural factors or independent variables that influence or cause a change in one or more dependent variables. The Chapter 3 section on “Creating Science” provides a detailed discussion of the basics of structural causal models. These models are usually a simplified view of the causes of the situation under study, normally limited to one dependent variable and a handful of the most important independent variables. This simplification of the reality surrounding the situation is known as being parsimonious. These parsimonious models are normally linear models and, once populated with data, may be solved with qualitative techniques (see Box 7.1 below and Chapter 9). However, when significant data is available, they usually are solved using quantitative statistical techniques such as means tables, regression analysis, factor analysis, maximum likelihood regression, and so forth. Structural causal models also may be quite complex, either linear or nonlinear, when they depict more than one dependent variable, in addition to including a number of antecedent, independent, and intervening variables (Chapter 3). Although it is possible to solve these complex models with qualitative techniques, they usually are solved with advanced statistical techniques (structural equation modeling, etc.). Structural causal models are used to describe, explain, and predict situations.

Academic researchers make wide use of structural causal models. Although security analysis practitioners may find less use for these models, they are a possibility when the situation under study requires explanations or predictions. Analysts first must conduct an information search (Chapter 5) of the situation under study to uncover what structural causal models already exist and have been used previously to answer the same or similar research questions. The analyst may find he/she needs to add more variables to existing models or even merge two or more existing models to allow the explanation or prediction called for in their research questions. After studying the situation in depth, analysts can draw on their own logic and reasoning in deciding to add additional variables to an existing model or create a new alternative model.

When an analyst develops a structural causal model, he/she initially uses the material from their information search and identifies independent variable(s) used in other studies that have shown promise for explaining the variance (changes) in the dependent variable. Analysts also can include other independent variables in their structural causal models, when information and logic lead them to think the variables will help explain or predict the variance in the dependent variable. For any subsequent review of their research by other analysts or supervisors, analysts should explain the logic and reasoning for including variables in the model. Likewise, the analyst also should justify why any variables were removed from existing models.

Finding the causal mechanisms in a structural causal model is extremely important. Causal mechanisms normally reside below the level of the variables themselves and, when identified, provide the explanation for how the independent variable causes the change or condition in the dependent variable. The causal mechanism may not be operationalized (or measurable), but its conceptual existence explains the effects the independent variable has on the dependent variable. For example, one postulate (a theoretical proposition repeatedly supported by empirical data) of Democratic-Peace Theory offers that two democratic states will not go to war with each other. The causal mechanism for this postulate explains how when both states are democracies, they tend to avoid war as both states view the other side as sharing similar democratic values, including the values of cooperation and compromise in resolving interstate disputes. The independent variable for this postulate’s theoretical proposition would be “political system,” and one nominal measure of this variable would indicate if both states in an interstate conflict are democracies.

Structural Causal Model Example. A meta-analysis compiles the results from past research on a subject and determines which components (factors, variables) are strongest at explaining or predicting the situation under study. In Nations at War, U.S. political scientists Daniel S. Geller and J. David Singer provide a meta-analysis on the causes of interstate war.²⁷ Geller and Singer’s study compiled two centuries of data and analyses on the causes of war. Their study developed a number of models for war-prone states at different levels of analysis (individual states, dyads, regions, and alliances) that—based on the independent variables in past studies that contained the most empirical support—explain how past wars started. The war-prone models can be used for explaining past and predicting future wars.

The Geller and Singer model for predicting war-prone dyads (2 states) is summarized below.²⁸ Their work reveals that within the many theorized causes of war over the last two centuries, the independent variables listed below have the strongest empirical support and thus are the most compelling to explain and predict war outbreaks. This model is stochastic and linear.

Dependent Variable (Y):

Y1 = Likelihood of Two States Going to War

Independent Variables (X):

X1 = Static Capability Balance

Theoretical Proposition: Two states near parity in static capability balance (territory + population + military capabilities + economic output) are more likely to go to war. This supports Power Preponderance Theory.

X2 = Dynamic Capability Balance

Theoretical Proposition: Two states with recent significant changes in their capability balances are more likely to go to war, which supports Balance-of- Power Theory and defines the Security Dilemma. The Security Dilemma offers that if a state increases its military capabilities to increase its security posture, it actually may be decreasing its security because neighboring states may become concerned about being attacked by the state that increased its military capabilities.

X3 = Contiguity/Proximity

Theoretical Proposition: Two states sharing borders or located short distances apart are more likely to go to war. This proposition is supported by empirical fact.

X4 = Regimes (Political Systems)

Theoretical Proposition: If one or both of two states are not democratic regimes, they are more likely to go to war. This supports Democratic-Peace Theory.

X5 = Economic Development

Theoretical Proposition: If one or both of two states do not have advanced economies (that is, industrialized, technology-based, diversified, etc.), they are more likely to go to war. This supports Liberal Commercialism Theory.

X6 = Enduring Rivalries

Theoretical Proposition: Two states with recent conflicts or historically enduring rivalries are more likely to go to war. This proposition is supported by empirical fact.

X7 = Alliances

Theoretical Proposition: Two states that are members of unbalanced external alliances are more likely to go to war. This supports Balance-of- Power Theory.

Geller and Singer’s War-Prone Dyad Model may be diagramed as a structural causal model as shown in Figure 7.16. This figure is an Ishikawa (or fishbone) model that employs the key characteristics of Capabilities, Geographic, and Political/Economic and places the above independent variables with their appropriate characteristic.

Additionally, Geller and Singer’s model depicts a comparative theory, meaning it can be used across a number of different case studies to explain the causes of war or to predict war outbreaks. Comparative theories do not assume every independent variable in the model will necessarily apply or have the same explanatory strength in every case study. Thus, explanations and predictions for dyadic wars may be generated using one or more of the independent variables noted in the Geller and Singer model. Structural causal models lead to hypotheses that the analyst can test to see if they are supported or not. It is the analyst’s responsibility to determine which of the model’s hypotheses are supported in a particular case study. Equifinality is the conceptual term for where there is more than one path (i.e., different combinations of independent variables and/or hypotheses) to explain or predict changes or conditions in the same dependent variable.

Using Geller and Singer’s War-Prone Dyad Model, Box 7.1 provides a case study of the period before the start of the 1980 Iran-Iraq War. In this case, security analysis customers would have wanted to know if a war could erupt. The study employs a qualitative pattern-matching technique where information supporting each hypothesis is sought to explain (and, in this case, predict) changes or conditions in the dependent variable, i.e., whether war would break out. In other words, does the pattern of information support the model? Additional discussion of pattern matching can be found in Chapter 9.

Agency Models

As highlighted above, security analysis projects often require a combination of basic, geospatial, temporal, process, structural causal, and agency models. Agency models are created after psychobiographies and assumption analyses are completed (Chapter 6). Agency models assist in explaining a decision or behavior. By allowing development and rank ordering of alternative decisions or behaviors, agency models also are useful for predictive analysis. Beyond the Chapter 6 points-of-view, assumptions and Critical Belief Analysis techniques, there are a number of additional agency modeling techniques useful in security analysis. This section looks closer at some of the most-used modeling techniques including Rational Choice Theory, Decision Theory, and Game Theory. These techniques are supported by efforts to determine alternatives (Chapter 8) and sometimes assist with and often provide interpretation and inference analyses (Chapter 9) that result in analytic findings.

Rational choice theory. This theory is a powerful analytic tool that is considered a formal agency modeling method because of its ability to systematically capture complex behaviors. Rational Choice Theory is used to develop new theory by uncovering the causal mechanisms associated with certain human behaviors. It also is used as an analytic framework in case studies to explain and/or predict human decisions and behaviors. Rational choice analyses include not only the points of view and assumptions of the target decision maker(s), but also the points of view and assumptions that analysts themselves make in explaining or predicting social behavior—something few other theoretical approaches can claim. Rational Choice Theory is grounded in several general assumptions:²⁹

1. Agents (i.e., decision makers) are purposive, goal-oriented, utility- maximizers. Utility entails the benefits the agent expects to receive from the situation and often is measured in financial gains or losses; it also can include other items the agent values such as territory, property, reputation, trust, security, love, lives saved or lost, jail term lengths, probabilities of success, and any other item of value to the agents. When utility cannot be measured quantitatively, it may be measured relatively on an ordinal scale; for example, ranging from 1 (worst) to 4 (best), 0 (worst) to 100 (best), or by nominal letter designations. Agents may be a single decision maker or a group of decision makers who work in unison.
2. Agents have a set of hierarchically ordered preferences, for which utilities can be assigned.
3. An agent’s ordered preferences are complete (i.e., they include all likely alternative behaviors) and also transitive (i.e., if A > B > C, then A > C, when B is eliminated).
4. In choosing among preferences, agents make rational calculations based on their ordered preferences, information levels, and levels of risk aversion. The agent will not always pick the preference with the highest utility if the associated risks (costs and consequences) for that preference are above their level of risk acceptance. The decision maker continually assesses costs, benefits, and consequences of making a decision.

Using the above assumptions, a multitude of Rational Choice analyses, including formal strategic games, may be devised to develop theory and to explain and/or predict human decisions or behaviors. In the past, security analysts often resisted employing Rational Choice Theory as they argued it is too academic. However, without realizing it, most security analysts have been using the assumptions and other tenets of Rational Choice Theory for years. For example, Rational Choice Theory’s general assumptions are the foundation for a number of other theories for agency analysis discussed in this section, including Prospect Theory, Decision Theory, and Game Theory.

Rational Choice Theory offers several types of rationalities:

1. Value-based rationality—when the agent’s actions (decisions or behaviors) are based only on the agent’s beliefs, morals, or values, without regard for the consequences.
2. Traditional rationality—when the agent’s actions are based on traditional behaviors without any considerations of why the actions took place or their consequences.
3. Instrumental rationality—when the agent’s actions are based on achieving a goal or objective, and the agent is concerned with the consequences of the behavior—this is where Rational Choice Theory and its related theories are used.

In Rational Choice Theory analyses, there are two important considerations the analyst should assess: (1) information levels and (2) risk levels. Information levels consider whether the agent has full information on the decision situation. Security leaders frequently make decisions in situations of uncertainty or where information is incomplete. In the Box 2.1 Cuban Missile Crisis analysis, it was shown how President Kennedy expanded the information search after his first day of meetings with the ExCom. Still, the U.S. did not know about the Soviet nuclear- capable, short-range bombers and tactical nuclear weapons already in Cuba. At the same time, Soviet Premier Khrushchev was making decisions without having full knowledge of the situation. Information levels may be assessed as:

1. Complete—when the agent has full information on all relevant functions (utilities, preferences, etc.).
2. Incomplete—when one or more information items are not known, normal in security decision making.
3. Perfect—when the agent has complete information, plus knowledge of what has happened in the past up to the decision point; this is seldom the case in security decision making.
4. Imperfect—when someone (i.e., the opposing player) has done something or has some capability the agent does not know about, which is a form of deception.

Risk levels are connected to an agent’s tendency toward risk acceptance or risk aversion. As can be imagined, different decision makers take different approaches to risk. Prospect Theory (discussed more below) explains how many decision makers assess risk in an asymmetric manner, with some tending to give more credence to potential loss over potential gain. For example, before approving a 1954 U.S. covert operation to overthrow the government of Guatemala, President Eisenhower asked his CIA Director Allen Dulles the chances for the operation’s success. Dulles’s reply: “about 20 percent.” Eisenhower thanked Dulles for being straight with him, and approved the covert operation. Before becoming President, Eisenhower was the Allied Supreme Commander responsible for planning and directing World War II invasions and campaigns in North Africa and Europe, where tens of thousands of U.S. and Allied soldiers died. He was by nature loss and risk acceptant. The Guatemala covert operation was a success.³⁰ Decision-making risk levels may be assessed with:

1. Certainty—when the agent knows what will happen.
2. Risk— when there is a good probability the agent knows what will happen.
3. Uncertainty— when there is a good probability the agent does not know what will happen.

Rational Choice Theory models are characterized as either parametric or strategic. A parametric model assumes knowledge of certain parameters and distributions. This model is used widely in economic analysis and is based largely in Decision Theory (discussed in more detail below). Parametric models are anchored in general Rational Choice Theory assumptions and include additional tenets that:

1. The outside world is a static-given; i.e., markets, institutions, structures, etc., already exist. (Note: Markets do not work without existing public goods such as infrastructure, property rights, contracts, etc.)
2. Agents normally consider information levels are complete, but may also consider decision making under certainty, risk, or uncertainty levels.
3. Usually deal with one agent, simple cost-benefit analyses, and short-term analyses.

Strategic models look at one or more agents’ short- or long-term goals and the means to achieve them. They are used widely in the non-economic social sciences, in particular in political science, and are based largely in Game Theory (discussed in more detail below). Strategic models usually capture the interactions of two or more agents. These models are anchored in general Rational Choice Theory assumptions and include the following tenets:

1. Agents look to maximize behavior (or utility) in context of interdependence; that is, interactions with and restraints resulting from other agents (actors, players).
2. Agent beliefs may be more important than their preferences.
3. Agents deal largely with strategic uncertainty.
4. Models tend to explain agent action or decisions by revealing causal mechanisms in a situation.
5. Models often involve more than one agent participating in either competitive or non-competitive games.

To conduct Rational Choice Theory strategic analyses, the analyst must be able to model three key items:

1. The numbers and identities of agents involved and their utility functions.
2. The interactions of competing agents, their information structures, and risk tendencies.
3. Estimates of likely outcomes, consequences, or equilibriums. An equilibrium is an outcome that is stable and where no player has incentive to take some other action.

Note: The analyst need only develop item number 1 above for parametric analyses.

Analysts often conduct basic Rational Choice Theory analyses when the situation does not fit the conditions for more complex theories such as Decision Theory or Game Theory, both discussed below. Basic Rational Choice Theory analyses took the form of a critical-thinking framework even before the emergence of more recent critical-thinking interest. Using a simple list-modeling technique, a basic Rational Choice Theory analysis can be quite powerful. There are five general, sequential steps used in conducting a basic Rational Choice Theory analysis:

Step 1: Identify the specific research question(s) (Chapter 4), determine the agents involved, and determine the decisions, decision implementations, or other behaviors the specific research question(s) seek.

Step 2: Identify the agents’ goals or objectives in the situation. Perform an information search (Chapter 5) and points-of-view and assumptions analysis (Chapter 6) to determine how the agents perceive the situation. Estimate the agent’s utility functions.

Step 3: Provide a complete range of alternative preferences (preferred decisions or actions) agents may consider to reach their goals or objectives (Chapter 8). Preferences should be included if there is any likelihood the agents may consideration them.

Step 4: Determine the likely successes, outcomes, and consequences (intended and unintended) for each preference (Chapters 9 and 10). Consider the agents’ information levels and risk aversions as part of this step.

Step 5: Using analytic techniques described in Chapter 9, identify the most likely preference(s) the agent will select. Rank order the preferences (highest to lowest). For a basic Rational Choice Theory analysis, a simple ordinal ranking of the agents’ preferences (1, 2, 3, etc.) is sufficient. Rational Choice Theory does not assume the agents will select the highest- ranked preference; thus, the analyst may find there are two or more potential agent courses of action. This is where considering the agents’ information levels, risk aversion, and the action’s consequences is so important. See Chapter 10 for additional Warning Analysis techniques when an intelligence analyst has to consider several potential agent courses of action.

Rational Choice Theory has received significant criticism over the decades. The most cogent of these criticisms come from the work of cognitive psychologist Daniel Kahneman and his colleague Amos Tversky. In 1979, they developed Prospect Theory, which highlighted how agents often do not make strictly cost- benefit decisions due in part to the agent’s loss-aversion tendencies. Loss aversion is the condition where an agent values avoidance of losses more than gains of similar amounts. For example, an agent may assess a $100 potential loss as equivalent to a $200 potential gain. In his later works, Kahneman highlighted how rationality is side-tracked as agents will employ one or more heuristics (or cognitive biases) to reach a decision (Chapter 2 and Appendix II). For a combination of his work on Prospect Theory and decision-making heuristics, in 2002 Kahneman was awarded the Nobel Prize in Economics. His and Tversky’s work called into question Economic Man Theory (Homo Economicus), the bedrock of neo-classical economic theory, which assumed agents made purely rational decisions to maximize their utilities. Their work questioned the validity and effectiveness of Rational Choice Theory parametric models.

This brings to mind the idiom of “do not throw the baby out with the bathwater.” In other words, all Rational Choice Theory should not be discarded based on Kahneman and Tversky’s research. They did not address Rational Choice Theory strategic models. The purpose of any modeling is to allow insights in the description, explanation, and prediction of decisions, behaviors, or conditions, which Kahneman and Tversky did not disprove for strategic models. Rational Choice Theory strategic models include consideration of points of views, assumptions, and beliefs, in addition to assessing how agent’s beliefs may be more important in a decision situation than their actual preferences. Kahneman and Tversky’s work is addressed as part of the cognition and reasoning filters in the Figure 6.1 decision-maker mental model. While recognizing the power of Kahneman and Tversky’s work, Rational Choice Theory strategic models systematically capture complex behaviors, in particular multi-agent interactions; they also assist in uncovering causal mechanisms in strategic situations. Rather than avoid Rational Choice Theory models, it is wise when employing them to keep Kahneman and Tversky’s work in mind.

Finally, do not confuse Rational Choice Theory analyses as being based on the need for the agent to be “rational,” as defined by traditional Western ethics and values. Rational Choice analysis simply offers that an agent has goals and objectives and can develop a prioritized list of preferences or courses of action to achieve those goals and objectives. For example, under the tenets of Rational Choice Theory, Saddam Hussein could be considered rational in ordering the 1980 start of the Iran-Iraq War (see Boxes 6.3 and 7.1), even though his decision for war ended with approximately 1.5 million soldier and civilian deaths. Indeed, Hussein had goals to prevent the spread of the Iranian Revolution to the Iraqi majority Shia Muslim population and to gain oil-rich lands from Iran. His preference to reach his goals was to go to war with Iran. Few would call Hussein’s actions rational, as they did not coincide with international “just-war” doctrine. In addition, he also violated the ethics and values of Western nations. His actions were further condemned after he deployed chemical warfare agents against the Iranian people, as well as some Iraqis, during the war. Still, the analysis of Hussein’s behavior fits into the Rational Choice Theory framework as he had goals and objectives and developed preferences (a plan of action) to achieve them.

Decision Theory Models. Explaining and predicting agent choices in conditions of uncertainty is the focus of the Rational Choice Theory-related field of Decision Theory. Normative Decision Theory is used to explain and predict as it analyzes the outcomes of decisions and highlights optimal decisions. Its models include a number of mathematical, statistical, and matrix techniques. Descriptive Decision Theory determines the process of how agents actually make decisions. In this section, two Normative Decision Theory techniques are discussed from the sub-fields of Utility Theory and Decision Trees.

Utility Theory. In his book The Thinker’s Toolkit, retired CIA analyst Morgan D. Jones describes the essence of utility:

…[It] is the benefit that someone received, is receiving, or expects to receive from some situation. It is what that person has gained, is gaining, or expects to gain. It is the reason why that person has taken, is taking, or will take certain action. Utility is the profit, the prize, the dividend, the trophy, the advantage, the motive, the goal, the objective, the hope….³¹

Utility Theory analyses focus on the calculation of expected values, which can be used to rank order a set of decision options. An expected value is a combination of a utility value for each decision option and the probability that a decision option will result in a prescribed outcome. The steps of a Utility Theory analysis include:³²

Step 1: Identify whose perspectives are being analyzed.

Step 2: Identify the options, alternative decisions, or courses of action as well as potential outcomes for each perspective.

Step 3: Construct a utility tree (see below) or a utility matrix (preferred).

Step 4: Assign utility values for each option-outcome combination. Ask the Utility Question: If this option is selected and this outcome occurs, what is the utility from the perspective of …? Utilities usually are measured in dollars or other quantitative measures, if available. If the utility cannot be quantified, relative values can be based on a scale of 0 to 100. When relative values are assigned, at least one option-outcome must have a relative value of 100. This is usually the agent’s most desired option- outcome and allows a relative comparison of other options-outcomes.

Step 5: Assign a probability to each outcome. Ask the Probability Question: If this option is selected, what is the probability this outcome will occur? Probabilities are based on values of 0 to 1.0 and can be calculated or estimated by the analyst. The probabilities for all outcomes for a single option must add to 1.0.

Step 6: Calculate the expected values by multiplying each utility by its probability and then adding the expected values for each option to obtain a total expected value for that option (see Box 7.2).

Step 7: Determine the ranking of each alternative option, decision, or course of action.

The Box 7.2 utility analysis matrix example provides a better understanding of this technique. This example refers to the options and outcomes in Box 2.1 on Cuban Missile Crisis U.S. decision making from the perspective of President Kennedy.

Utility Theory analyses are flexible. The analysis below also should undergo a sensitivity analysis; that is a technique where adjustments (changes) are made to the estimated relative utility values and estimated probabilities based on alternative assumptions or different data and the total expected values recalculated. This allows the analyst to determine how robust the initial results are under different assumptions or estimates.

Advanced utility analysis allows the inclusion of multiple goals, multiple options, and multiple players. Box 7.2 displays a utility matrix analysis for one agent (Kennedy) and for one goal or objective (a combination of removing the missiles and avoiding war). Utility analyses are flexible and may be used for an agent with multiple goals or one who defines their goals differently in the same situation. For example, the Box 7.2 goals could have been separated into individual goals of (1) removing the missiles and (2) avoiding war. A third goal also could be included of protecting West Berlin from Soviet invasion. When an agent has more than one goal or objective, an individual utility matrix analysis is prepared for each goal or objective. These matrixes can then be merged to reveal the expected values for several goals and allow an even more-rigorous analysis of one agent’s decision options. At times, there also may be two competing agents (i.e., Kennedy and Khrushchev). In this situation, a utility matrix analysis can be performed on each agent and each of their goals, then merged into one matrix analysis table. Jones’s The Thinkers Toolkit provides excellent descriptions of both basic utility analyses (one agent, one goal) and advanced utility analysis (multiple agents, multiple goals).

Decision Trees. These are models that graphically depict the choices and outcomes at different points in alternative sequences or chains of events. They are called “trees,” but may be displayed in tree, flowchart, matrix, or other graphical formats. An events tree generates a descriptive diagram of a sequence of events. A decision tree depicts a similar sequence of events with additional information to inform or explain decisions. Probability trees are used widely in decision making because they allow the analyst to apply probabilities to the sequence of events diagrammed in events trees or decision trees.

When building an events tree or decision tree, the analyst should ensure the scenario events/decisions are mutually exclusive, meaning the events/decisions cannot overlap. They also must ensure the events/decisions are collectively exhaustive, meaning they include every potential event or decision in the scenario. Events trees and decision trees allow a structured, systematic analysis that reveal the following:³³

• Dissection of a scenario into its sequential events.
• Cause-and-effect linkages, indicating which decisions or events preceded and followed others.
• Which decisions or events are dependent on others.
• Which linkages are strongest and weakest.
• Visual comparison of how one scenario differs from another.
• Range of alternatives that might otherwise remain hidden.

Figure 7.17 is a decision tree in flowchart format of the war decisions made by the Germans from 1914-1917. In June 1914, Archduke Ferdinand of Austria- Hungary was assassinated by a Bosnian-Serb nationalist. In July 1914, Austria- Hungary declared war on Serbia. Germany’s first decision was whether to join the war on the side of Austria-Hungary, in accordance with an existing mutual- defense treaty, which it did. Russia joined the war on the side of Serbia also in accordance with a mutual-defense treaty. Germany’s next decision was whether to declare war on Russia, which they did, activating a mutual-defense treaty between Russia, Great Britain, and France. The United States joined the war in April 1917 after the Germans conducted unrestricted submarine warfare in the Atlantic and attacked several U.S.-flagged ships. Figure 7.17 depicts that the German decision to declare war on Russia was the key factor in the expansion of the conflict into World War I from what started as a regional war between Austria-Hungary and Serbia. The war resulted in 20 million deaths: nine million military, 11 million civilians, plus another 20 million wounded. World War I highlighted the dangers of unbalanced mutual-defense treaties that pull states into unwanted conflicts.

Probability trees are used when the analyst must rely on estimates and not facts. Figure 7.17 is based on historical facts. When Germany was making its war decisions, its leaders would have been relying on well-known outcomes of those decisions. Germany’s leadership knew with some certainty that declaring war on Russia would result in Great Britain and France joining the war. If the Germans had not known other states’ likely actions, a probability-tree analysis would have been needed.

Probability trees must meet the same basic parameters of event and decision trees. To employ probability trees, security analysts should understand the basics of Probability Theory. In general, people often are not comfortable with probabilities. This is especially true when faced with estimating probabilities involving two or more events. In some situations, probabilities can be computed easily. For example, in a full deck of 52 cards there is one Ace of Hearts, so a person can calculate the probability of drawing an Ace of Hearts from a full deck of cards is 1 in 52 or .019 (1.9%). Probabilities are used widely in security analysis, including with sampling theory (Chapter 3), probability trees, statistical analyses, warning intelligence analysis (Chapter 10), and for estimating likelihood and confidence levels in analytic findings (Chapter 11). Box 7.3 provides an example of a probability tree and includes additional information on Probability Theory.

Box 7.3

Probability-Tree Example: Hypothetical Hostage Rescue

Terrorists kidnap 50 civilians. The commander of a special operations unit asks the unit’s intelligence officer to calculate the probability of whether all the kidnapped hostages will die if a rescue mission is mounted. The intelligence officer starts with constructing a probability tree considering the following: 1. The success or failure of the special operations team to reach the terrorist location. 2. An attempt by the terrorists (yes or no) to booby-trap the kidnapped hostages with explosives. 3. The likely death of the kidnapped hostages (ranging from all to none) due to engagements between the terrorists and special operations team during a rescue mission. Referring to historical frequency-and-experience data of previous hostage rescue missions, there is a .9 probability of the team reaching the terrorist location, and a .3 probability the kidnapped hostages will be booby-trapped with explosives. If the kidnapped hostages are booby-trapped, there is a .4 probability all hostages will die during the rescue mission, a .4 probability some will die, and a .2 probability none will die. If the kidnapped hostages are not booby-trapped, there is a .2 probability all hostages will die, a .2 probability some will die, and a .6 probability none will die. The probability tree is constructed as follows: This hostage rescue analysis requires computations of probabilities associated with a complex situation involving multiple outcomes. If the rescue mission is launched, there are only two outcomes: either (1) the rescuers locate the hostages, or (2) the rescuers do not locate the hostages, ending the rescue mission. Locating the hostages (event A) or not locating the hostages (event B) are two disjointed or mutually exclusive events. Event A and event B are also collectively exhaustive since they are the only possible events associated with locating the hostages once the mission is launched. The probability of event A added to the probability of event B must equal 1.0. As depicted above, the analyst estimates there is a 0.9 probability of locating the hostages (event A) and; therefore, there is a 0.1 probability the hostages will not be located (event B). Keep in mind in the example above that the commander wants to know the probability of whether all of the hostages will die if a rescue mission is attempted. With this objective in mind, the analyst is interested mainly in branches of the probability tree emanating from the “locate hostages” node. Now, suppose that once they are located, the analyst estimates the probabilities as to whether the hostages will be booby-trapped or not. These two possibilities are also mutually exclusive and collectively exhaustive. Frequency-and-experience data reveals a probability the hostages will be booby-trapped is .3, and thus the probability of not being booby trapped must equal 0.7. The analyst further determines that there are three mutually exclusive outcomes that can occur in an engagement between the terrorists and special operations personnel: (1) all of the hostages will die, (2) some of the hostages will die, or (3) none of the hostages will die. As depicted above, the analyst has estimated the conditional probability all hostages will die given they are booby-trapped (.4) is twice as likely as the conditional probability all hostages will die given they are not booby-trapped (.2). Analysts are frequently called upon to work with such conditional probabilities, defined as: 𝑃(𝐴|𝐵) = P(A ∩ B)/p(B) . That is, the probability of A given B is equal to the probability of A and B divided by the probability of B. Since the commander in the hypothetical example is interested in knowing the probability of whether all the kidnapped hostages will die as a result of a rescue mission, the analyst must consider all possibilities that might lead to the deaths of all hostages once they are found. The probability decision tree above makes it easy to see the computations required. Once the hostages are found, there are only two ways all of the hostages will die: (1) they are booby-trapped and they all die, or (2) they are not booby-trapped and they all die. Clearly, both of these situations are joint events. To compute the probabilities of these joint events, one must return to the definition of conditional probability. From that definition, it is apparent that 𝑃𝑃(𝐴 ∩ 𝐵) = 𝑃(𝐴|𝐵)𝑃(𝐵). Thus, to find the probability that the hostages are booby-trapped and they will all die is equal to the conditional probability all hostages will die given they are booby-trapped multiplied by the probability the hostages are booby-trapped; which yields (.4)(.3) = .12. Likewise, the probability the hostages are not booby-trapped and they will all die is equal to the conditional probability all hostages will die, given they are not booby-trapped multiplied by the probability the hostages are not booby-trapped: (.2)(.7) = .14. Thus, the probability that all hostages die, given their rescue in undertaken, is equal to .12 + .14 = .26. (This calculation is not separately depicted on above probability decision tree.) Because the commander is interested in knowing the probability that all the kidnapped hostages will die as a result of a rescue mission, the analyst must compute the probability that all hostages will die and the rescue mission is undertaken. Again, conditional probability must be employed. Since 𝑃(𝐴 ∩ 𝐵) = 𝑃(𝐴|𝐵)𝑃(𝐵), it follows that P (all hostages will die if the rescue mission is undertaken =.26) multiplied by the probability the rescue mission team locates the hostages (.9). In this scenario, the probability that all hostages will die if a rescue mission is undertaken equals (.26)(.9) = .234. The probability tree above allows for an organized and clear picture of the computations required to answer the commander’s question in this scenario. It depicts how probabilities for mutually exclusive events are added and conditional probabilities multiplied to reach the results. The probability-tree analysis reveals a .234 probability that, if a rescue mission is mounted, it would result in the death of all hostages. There is; however, also a .234 probability that only some (not all) of the hostages will die, and a .432 probability none of the hostages will die in an attempted rescue mission. In conclusion, the intelligence officer finds that historical frequency-and- experience data reveals when no hostage rescue mission is mounted, in .30 (30%) of the cases all hostages die. Should the intelligence officer recommend the commander order the hostage rescue mission? This is where information levels and risk levels should both be considered.

Bayesian analysis. When working with probability trees or otherwise dealing with estimates or probabilities that may change, Bayesian analysis addresses conditional probabilities and allows probabilities to be updated when new information becomes available. This analysis employs Bayes’ Theorem, named for its creator English theologian, philosopher, and mathematician Thomas Bayes (c. 1701-1761).

Bayesian analysis is the technique used by casino card counters playing Blackjack (21), who know there are only four cards of each value in a single full deck of playing cards. The card counters keep track of how many low cards (3s to 6s) and high cards (9s to Aces) have been played and thus can estimate how many low or high cards are left in the deck. The card counters then use this updated information to revise the probabilities a low or high card will be drawn next. Card counters determine their playing and betting strategies based on the revised probabilities. The card counters do not have a calculator in their head to exactly calculate the revised probabilities based on Bayes’ Theorem, but they do gain an estimative or intuitive sense of how to place their bets with updated information gained from the card-counting. Card counters do not always win; but, by employing this intuitive sense of Bayes’ Theorem, they greatly increase their probability of winning. Experienced card counters can even be successful when multiple decks of cards are used in Blackjack. When identified, card counters usually are ejected from casinos or banned from Internet gambling sites.³⁴

While the philosophical foundations of Bayes’ Theorem are quite powerful, the mathematics are quite simple: it only requires addition, subtraction, multiplication, and division.³⁵ In its basic form, Bayes’ Theorem is an algebraic expression with three known variables that is solved to determine one unknown variable. The known variables include an estimated prior probability (x), a new condition treated as true (y), and a new condition treated as false (z). The new condition treated as true (y) may include new events, new information, or other conditions that require a revision of the prior probability. The new condition treated as false (z) compensates for when the probability of the new condition treated as true (y) is in fact false, such as when the new true condition does not occur. Bayes’ Theorem is employed to determine a revised (or posterior) probability for the situation under study using the following algebraic expression:

xy / xy + z (1-x) = Posterior Probability

Box 7.4 demonstrates the use of Bayes’ Theorem in a security analysis situation, in this case a continuation of the hypothetical hostage rescue analysis in Box 7.3.

Game theory models. Strategic situations where the outcomes result from the interactions and decisions of two or more agents is the province of Game Theory. Models generated by this theory capture how individual agents’ decisions are interrelated, including how one agent’s decisions or behaviors depend on other agents’ decisions. Game Theory models are used widely in political science, economics, and other social sciences. This technique generates abstract models (or games), which may not be accurate depictions of the real world, but do provide insights into multi-agent decisions and behaviors modeled. Game Theory models are created in two forms: extensive form and strategic form. An extensive-form game (depicted in trees or flowcharts) details each agent’s (or player’s) choices, the order and consequences of their choices, how they evaluate those consequences, and what they know when they make a decision. Extensive- form games can be reduced to strategic-form games (depicted in matrix models), which add the players’ corresponding game-playing strategies and visually depict the interdependent structure of the game. This section will focus on strategic- form games.

Strategic-form games have a common set of components. In these games, two or more players may have similar or different goals or objectives from which they develop similar or different strategies to achieve outcomes as they play the game against other players. In accordance with the assumptions of Rational Choice Theory, each player develops utilities for particular outcomes that are called payoffs. Typically, all players are assumed to know other players’ payoffs. Uncertainty is injected into a game by what is known as information sets as to whether the game is played under perfect information, complete information, or incomplete information. Games may be single-play or iterated (multiple-play). Games may be cooperative, where players can communicate and make agreements, or they can be non-cooperative, where players usually do not communicate and do not make agreements. Analysts look for equilibriums in strategic-form games; that is, where payoffs identify the best results for both players.³⁷ Equilibriums assist in determining the most likely outcomes of a game.

Prisoner’s dilemma (single play). Figure 7.18 provides an example of a common game used in security analysis known as Prisoner’s Dilemma. Those who have watched police/detective movies or television shows will recognize the concept of when two suspects for a crime are placed in separate interrogation rooms. The police know they do not have enough evidence to convict both suspects of the crime, so they need one or both to confess to the crime. Each suspect is told if they confess and blame the crime on their fellow suspect, they will receive a reduced sentence or possibly be set free, while the police will “throw the book” at their fellow suspect. Prisoner’s Dilemma is a two-player game with each player having the same two strategies: defect (confess) or cooperate (stay silent).³⁸ It is a single-play, non-cooperative game as the two suspects are not allowed to communicate or make agreements. In the model below, if one suspect confesses and one stays silent, the confessing suspect is set free, and the silent suspect gets 10 years in jail. If both suspects confess, they both get 5 years in jail. If both suspects stay silent, they both get 1 year in jail on a lesser-included offense. The outcome of this single-play game depends on whether one or both players decide to select a defect strategy based on their own self-interests (to reduce jail time); or, if they decide to stay silent and cooperate (with the other player) because of strong bonds of loyalty and trust between the players. In Figure 7.18, the game has a dominate strategy equilibrium for both players to remain silent as this provides the least total years in jail for both players combined. A causal mechanism related to self-interest; however, may drive one or both players’ decisions as they confess to try and be set free.

Prisoner’s Dilemma may be used in any security analysis single-play situation with two players, where each player has the same two strategies of either defect or cooperate. For example, China and the United States are rivals for world influence. Underlying the competition for world influence are similar goals of increasing markets for their economic products and being influential in international trade and financial institutions. To obtain a competitive edge over the United States, China may undertake an extensive aid program for underdeveloped states, establish trade agreements with multiple world states, and maneuver to increase their stature in international trade and financial institutions (a defect strategy). If the United States decides to cooperate and not match China’s actions, it could lose world influence to China. On the other hand, if the United States matches China’s actions (also defects), it will generate competition and likely not lose U.S. relative world influence. If both states decide to cooperate, they might both be better off because they could advance their world influence by working together and possibly avoid escalating their individual costs. This game hinges on the causal mechanisms related to each player’s views of its state’s national self-interests and whether they have developed enough reciprocity or trust to cooperate. It is a single-play, non-cooperative game because, while there are continuous interstate negotiations, each state decides separately on its long-term strategy. This model does not include areas of potential military conflict between China and the United States, such as over the status of Taiwan, which is better modeled as a Game of Chicken discussed below.

Prisoner’s dilemma (multiple-play). Figure 7.19 details a multiple-play, iterated Prisoner’s Dilemma game. What makes this version of Prisoner’s Dilemma a totally different game is that it takes place over a longer time period with multiple plays (or iterations) and is a cooperative game. The game may be played for an unlimited number of consecutive times. The players can communicate and make agreements, if they desire. The payoffs for this game are relative and designated by nominal letters. The dominant strategy equilibrium in this game is when both players cooperate because the payoff for both is to be rewarded (R) for their decisions. The worst payoff is when both defect and are punished (P) for their decisions. When one player defects and the other cooperates, the defector’s payoff is the utility for their temptation (T) or the payoff from the reason leading them to defect. At the same time, when only one player defects, the other is played for a sucker (S). The game assumes R > (T + S)/2. Research reveals the long-term best outcomes for any one player is when both players cooperate. Research also reveals that, in an iterated Prisoner’s Dilemma game, a player should always apply the same strategy on their next move as the other player applied on their last move—meaning cooperation should be followed with cooperation, and defection should be followed by defection—this best-play strategy is named Tit-for-Tat. This game is used across the social sciences; but, is particularly appropriate in recurring situations of international trade agreements, security conflicts, or other long-term diplomatic negotiations.

In his book The Evolution of Cooperation, U.S. political scientist Robert Axelrod analyzes a situation of iterated Prisoner’s Dilemma that emerged spontaneously in the front-line trench warfare of World War I.³⁹ After several months of frontal assaults between British, French, and Allied forces and the opposing Germans, the war settled into a stalemate of trench warfare stretching for hundreds of miles across western France and Belgium. Trench warfare found opposing forces occupying trenches only a few hundred yards apart. An iterated Prisoner’s Dilemma emerged spontaneously among small units on both sides of the front. The causal mechanism at work was that soldiers sought to avoid being killed in the stalemated trench warfare. Both sides fired on the opposing side in ways to do no harm to enemy troops as infantry riflemen and machine gunners fired over the heads of the enemy at targets or into areas not near enemy troops. Artillery units would sometimes defect, but would also normally fire into areas without enemy troops. This would be followed by a similar artillery assault by the other side using a Tit-for-Tat strategy. No verbal agreements were made between opposing forces except for the sense of reciprocity created by each side’s actions. It did not take long for the iterated Prisoner’s Dilemma to spread along both sides of the front such that entire opposing battalions were following the Tit-for-Tat strategy. The situation enraged the high commands on both sides of the front who expected aggressive action by their troops. The only way the iterated Prisoner’s Dilemma was broken was when both sides ordered assaults to storm the “no man’s land” between the opposing trenches.

Game of chicken. Another commonly used game in security analysis is a Game of Chicken,⁴⁰ named after the 1950’s male-youth game of two players driving their vehicles at high speed directly toward each other to see which player demonstrated the most “courage” by not swerving or “chickening-out” until the latest moment. The term is appropriate in security analysis when two players are barreling headlong into a potential conflict. Figure 7.20 details the classic Game of Chicken that occurred during the Cuban Missile Crisis.⁴¹ In a Game of Chicken the two players may have different strategies. The Figure 7.20 game reveals that the Soviets had two strategies: either keep the nuclear missiles in Cuba or withdraw them. President Kennedy and his ExCom developed their primary strategies of a naval quarantine or an air assault followed by a military invasion. This is a single- play, cooperative game. As was seen in Box 2.1, diplomatic negotiations between the Soviets and United States took place as the situation unfolded. The payoffs for this game are based on a relative ordinal scale of 1 to 4, where 1 is the worst outcome for a player and 4 is the best outcome for a player. The equilibrium for this game would have been for Kennedy to order a naval quarantine and the Soviets to withdraw the missiles, which was the actual outcome. This equilibrium results in payoffs to each player of 3, which are not the best payoffs for either player but avoids conflict, including a possible nuclear war, with the least desirable payoffs. This is a compromise situation. Combining the Figure 7.20 Game of Chicken with the Box 7.2 utility theory analysis of Kennedy’s decision making generates additional insights for explaining the outcomes of the Cuban Missile Crisis. This demonstrates how almost any security analysis situation likely will require multiple models to fully answer the research questions.

Key Concepts

Agency Models

Bayesian Analysis

Bayes’ Theorem

Causal Mechanisms

Comparative Models

Comparative Theory

Complex Systems

Conceptual Models

Concepts

Decision Theory

Decision Trees

Definitions

Deterministic Models

Dynamic Models

Equifinality

Event Trees

Expected Values

Extensive Form Games

Flowchart Models

Game of Chicken

Game Theory

Gantt Charts

Geospatial Models

Graphical Models

Ishikawa (fishbone) Model

Iterated Game

Linear Models

Linkage Models

List Models

Matrix Models

Meta-Analysis

Modeling

Network Analysis

Nonlinear Models

Organizational Models

Parametric Models

Parsimonious

Physical Models

Prisoner’s Dilemma Game

Probability Theory

Probability Trees

Process Models

Prospect Theory

Rational Choice Theory

Sensitivity Analysis

Simulated Models

Social Network Analysis

Solvable Models

Static Models

Stochastic Models

Strategic Form Games

Strategic Models

Structural Causal Models

System Models

Target Networks

Temporal Models

Time Series Analysis

Utility Theory

Discussion Points

1. Using the format in Figure 7.1, construct a conceptual model defining “democracy.” Are there different ways to conceptualize democracy? What are they? Appendix III may assist with your conceptualization of democracy.
2. Using Figure 7.6 for guidance, model the processes you follow from the time you awake until you arrive at school or work each morning. Convert your model into an Ishikawa (fishbone) model (Figure 7.11) and determine if there are ways to revise your processes and reduce the time between waking and arriving at school or work.
3. Assume it is the late-1980s and you are part of a U.S. joint interagency planning (policy) staff tasked with developing a U.S. counter-narcotics strategy targeting cocaine trafficking. Your intelligence colleagues are responsible for developing the target and threat assessments to support the strategy. Which of the modeling figures in this chapter would you recommend to your intelligence colleagues? Your policy colleagues are responsible for developing the strategy (actions plans) from the target and threat analyses. Which of the modeling figures in this chapter would you recommend your policy colleagues create? What models are missing as you complete your intelligence and policy work? How would you measure whether your strategy was successful?
4. Expand the analysis shown in Boxes 6.3 and 7.1 of a potential 1980 Iran-Iraq War by constructing a Game Theory model for a single-play game of the potential conflict between Iran and Iraq. Does the Game Theory model resemble a Prisoner’s Dilemma Game (Figure 7.18) or a Game of Chicken (Figure 7.20)? Why?

Notes

¹ Richard Paul and Linda Elder, Critical Thinking, Tools for Taking Charge of Your Professional and Personal Life, 2^nd ed. (Upper Saddle River, NY: Pearson Education, Inc., 2014), 360.

² David Robson, “There really are 50 Eskimo words for ‘snow,’ The Washington Post, January 14, 2013, https://www.washingtonpost.com/national/health-science/there-really-are-50-eskimo- words-for-snow/2013/01/14/e0e3f4e0-59a0-11e2-beee-6e38f5215402_story.html (accessed January 15, 2021).

³ Paul and Elder, 100.

⁴ Robert M. Clark, Intelligence Analysis, A Target Centric Approach, 5^th ed. (Thousand Oaks, CA: SAGE/CQ Press, 2017), 65.

⁵ Ibid.

⁶ Richard L. Kugler, Policy Analysis in National Security Affairs: New Methods for a New Era (Washington D.C.: National Defense University Press, 2006).

⁷ Clark, 66.

⁸ Ibid.

⁹ Ibid.

¹⁰ Ibid.

¹¹ Ibid, 67-68.

¹² Heritage Foundation, “Index of Economic Freedom,” https://www.heritage.org/index/ranking (accessed November 22, 2020).

¹³ Transparency International, “Corruption Perceptions Index,” https://www.transparency.org/en/cpi (accessed November 25, 2020).

¹⁴ Clark, 198.

¹⁵ Sarah Miller Beebe and Randolph H. Pherson, Cases in Intelligence Analysis, Structured Analytic Techniques in Action, 2^nd ed. (Los Angeles, CA: Sage/CQ Press, 2015), 222.

¹⁶ Ibid, 200-201.

¹⁷ Gantt.com, “What is a Gantt Chart?” https://www.gantt.com/ (accessed January 28, 2021).

¹⁸ United Nations Office on Drugs and Crime, World Drug Report 2010, https://www.unodc.org/documents/wdr/WDR_2010/1.3_The_globa_cocaine_market.pdf (accessed January 29, 2021).

¹⁹ Clark, 91.

²⁰ Ibid, 40.

²¹ Ishikawa (fishbone) models can employ as many key characteristics as the situation demands. In production management, it is common to use the 6-Ms: Methods, Manpower, Mother Nature, Materials, Measures, and/or Machines. In service management, it is common to use the 5-Ps: People, Places, Policies, Processes, and/or Procedures. The analyst is free to use these characteristics, mix and match characteristics, or develop other characteristics as the situation demands.

²² Clark, 92.

²³ General (retired) Stanley McChrystal, “It Takes a Network,” Foreign Policy, February 21, 2011, quoted in Clark, 42.

²⁴ Clark, 185.

²⁵ Ibid, 41.

²⁶ Modified from Ibid, 43.

²⁷ Daniel S. Geller and J. David Singer, Nations at War, a Scientific Study of International Conflict (New York, NY: Cambridge University Press, 1998).

²⁸ Ibid, 68-96.

²⁹ James D. Morrow, Game Theory for Political Scientists (Princeton, NJ: Princeton University Press, 1994), 7-8.

³⁰ Stephen Schlesinger and Stephen Kinzer, Bitter Fruit, the Untold Story of the American Coup in Guatemala (Garden City, NY: Anchor Books, 1982), 177.

³¹ Morgan D. Jones, The Thinker’s Toolkit, 14 Powerful Techniques for Problem Solving (New York, NY: Three Rivers Press, 1995), 246.

³² Ibid, 276.

³³ Ibid, 127-128.

³⁴ Nate Silver, The Signal and the Noise, Why So Many Predictions Fail—but Some Don’t (New York, NY: Penguin Books, 2012).

³⁵ Ibid, 240-249.

³⁶ This version of Bayesian analysis and format for this table from Ibid, 245-248.

³⁷ Morrow, 51-119.

³⁸ Steven J. Brams, Theory of Moves (New York, NY: Cambridge University Press, 1994), 127-130.

³⁹ Robert Axelrod, The Evolution of Cooperation (New York, NY: Basic Books, 1984), 73-87.

⁴⁰ Brams.

⁴¹ Ibid, 130-138.