COU 3: Terrorism as Signalling

In models of politics, “signalling” refers to behavior used to demonstrate some underlying trait or quality on the part of the signaller that is otherwise difficult to credibly communicate. In a remarkable number of settings, signalling turns out to be a plausible explanation for political behavior that otherwise seems irrational.

Consider terrorism, for instance. The groups that use terrorism as a tactic are often extremely weak relative to the nation-states they declare to be their enemies. Acts of terrorism by such groups, then, seem to have no prospects of achieving the groups’ stated aims, and thus may appear to be no more than expressions of deadly but ultimately impotent rage. In a study of political violence by militant, non-state organizations, however, Ethan Bueno de Mesquita (Bueno de Mesquita 2010) develops an explanation of terrorism as signalling. He proposes that insurgent groups, through terrorism, hope to persuade large numbers of persons to join or materially support them.

Why would terrorist violence by a militant organization persuade potential supporters to join or support the organization? Because complex attacks against civilians (for instance, coordinated suicide bombings occurring simultaneously in each of a several of cities) can only be successfully executed by a group of competent and disciplined conspirators. Thus, a sufficiently complex attack, when it is successfully carried out by an insurgent group, serves as a signal – i.e. it credibly demonstrates – that the insurgent group is competent, disciplined, and effective. Seeing a complex attack successfully executed, then, prospective supporters of the insurgent group will be persuaded that the group is competently and effectively led, and will thus be more willing to join or aid it. Bueno de Mequita, then, proposes that for militant organizations, terrorist violence is not merely an end-in-itself. It is in fact a way of signalling – i.e. communicating particular facts (i.e. the organization’s degree of competence, discipline, and effectiveness) to a particular audience (i.e. prospective recruits to and supporters of the organization).

In this COU, you’ll build and analyze a model of learning to depict a potential supporter of an insurgent group making inferences about the group’s competence by observing the success or failure of an attempted terrorist attack.

Imagine a militant organization that is waging an ongoing insurgency, and imagine a potential supporter of that organization. Imagine that the potential supporter at a particular moment in time is uncertain about two things:

The extent to which the organization is competent, disciplined, and effective.
Whether the next terrorist attack attempted by the organization will be successful.

“Successful”, of course, is a vague term. In this case, think of “successful” as any quality of a terrorist attack indicating that it was carried off as intended. For instance, an attack that is disrupted by the state’s security services so that it causes only minor injuries to a few persons is not successful, while an attack that is apparently un-anticipated by the security services and kills many victims is successful.

Prompt 1

Build a model of the potential supporter’s uncertainty using the Marginal-Conditional Method. More specifically…

Model the potential supporters marginal uncertainty about the extent to which the terrorist organization is competent, disciplined, and effective.
For each resolution of the marginal uncertainty you model in (i) model the potential supporter’s uncertainty about whether the next terrorist attack attempted by the organization will be successful, conditional on the knowledge that that resolution has occurred.

The model you build must satisfy all the following requirements:

First, you must specify the model by drawing a Marginal-Conditional Diagram.

Second, you must assign specific numerical values to all marginal and conditional probabilities in the model.

Third, your model must assume that there are only two possible resolutions of the uncertainty about whether the next attempted attack by the organization will be successful. Specifically, it must assume that the next attempted attack will either be “successful” or “not successful”.

Fourth, your model must assume that the probability that the attempted attack is “successful” conditional on any given extent of the organization’s competence/discipline/effectiveness is increasing in the extent of the group’s competence/discipline/effectiveness. For instance if in your model “abysmal” is one possible extent of the organization’s competence/discipline/effectiveness and “middling” is a higher possible extent of the organization’s competence/discipline/effectiveness, then your model must assign specific numerical values to the conditional probabilities P \left( \text{successful} \left| \text{abysmal} \right. \right) and P \left( \text{successful} \left| \text{middling} \right. \right) such that: P \left( \text{successful} \left| \text{abysmal} \right. \right) < P \left( \text{successful} \left| \text{middling} \right. \right)

It is entirely up to you to invent the exhaustive list of mutually exclusive possible resolutions of the potential supporter’s uncertainty about the extent to which the terrorist organization is competent, disciplined, and effective. Unlike the uncertainty about whether the next attack will be successful, you are free to assume any number of possible resolutions of that uncertainty (as long as that number is two or greater and finite!).

Make sure to label the axes of the diagram you draw in a way that makes clear which uncertainty each axis of the diagram depicts. Also make sure to label the sections of the diagram in a way that makes clear which resolutions of each uncertainty each section depicts.

Prompt 2

You’ve now modeled the potential supporter’s uncertainty at a particular moment in time about the competence/discipline/effectiveness of the organization and whether the organization’s next attempted attack will be successful. Now imagine a later moment in time, after the militant organization has attempted to carry off its next attack. Imagine the potential supporter has seen accounts and snippets of video of the attempted attack on social media, and from what he has seen knows whether the attempt was successful or instead not successful. In other words, imagine a later moment in time at which the potential supporter’s uncertainty about whether the next attempted attack will be successful has been resolved.

Part (a)

Re-draw the marginal-conditional diagram you drew in responses to Prompt 1. For each resolution of the uncertainty (as depicted in your model) about the extent to which the organization is competent, disciplined, and effective:

Write the probability assigned to that resolution by the potential supporter’s posterior beliefs in the event that the attack was successful. Write the probability as a fraction, not as a decimal number.
Mark up the diagram to show how you derived that probability.

Note that you are not required to simplify any fractions you compute. For instance, a completely un-simplified fraction like this… \frac {\frac{1}{8}\times\frac{2}{273}} {\frac{1}{8}\times\frac{2}{273} + \frac{2}{8}\times\frac{6}{82} + \frac{5}{8}\times\frac{9}{431}} …is perfectly fine as one of the probabilities written in response to (i), as long as it is correct!

Part (b)

Write the probability assigned to that resolution by the potential supporter’s posterior beliefs in the event that the attack was not successful. Write the probability as a fraction, not as a decimal number.
Mark up the diagram to show how you derived that probability.

Rubric

Prompt 1

A completely correct answer to this prompt meets all of the following criteria:

It is a Marginal-Conditional Diagram of uncertainty, in that it is a rectangle with the horizontal axis labeled as depicting one uncertainty and the vertical axis labelled as depicting some other uncertainty.
The horizontal axis is labeled in a way that makes clear that it depicts uncertainty about the extent to which the terrorist organization is competent, disciplined, and effective.
The vertical axis is labeled in a way that makes clear that it depicts uncertainty about whether the next attempted attack by the organization will be successful.
The horizontal axis is divided into two or more sections. Each of these sections (a) includes a label written at the top of the rectangle which clearly identifies that section as depicting one distinct resolution of the uncertainty about whether the terrorist organization is competent, disciplined, and effective, and (b) includes a label written at the top of the rectangle that gives a specific numerical value for the marginal probability of the resolution that section represents. Together, the specific numerical values written as marginal probabilities for the horizontal sections sum to 1.
Each section of the horizontal axis is divided along the vertical axis into exactly two sub-sections. One of these vertical sub-sections is labeled in a way that clearly indicates that it represents the event that the attack is successful. The other sub-section is labeled in a way that clearly indicates that it represents the event that the attack is not successful. Each vertical sub-section also includes a label that gives a specific numerical value for the probability of the event depicted by that vertical sub-section, conditional on the event representing the horizontal section containing that sub-section. Across the two sub-sections within each vertical section, the probabilities written sum to 1.
The specific numerical values written as conditional probabilities in the sub-sections are ordered relative to one another in a way that depicts the idea that the probability that the attempted attack is “successful” conditional on any given extent of the organization’s competence/discipline/effectiveness is increasing in the extent of the group’s competence/discipline/effectiveness.

If your response meets all of these criteria, it earns 8 points. Otherwise:

If it wholly meets criteria (i) through (v) but does not fully satisfy criterion (vi), it earns 4 points.
If it wholly meets criteria (i) through (iv) but does not fully satisfy criterion (v), it earns 3 points.
If it wholly meets criteria (i) and (iii) but does not fully satisfy criterion (iv), it earns 2 points.
It it fails to fully satisfy any of criteria (i), (ii), or (iii), it earns 0 points.

Prompt 2 Part (a)

Your answers to Prompt 2 can only be evaluated if your answer to Prompt 1 earns 4 points or more – i.e. only if your answer to Prompt 1 fully satisfies all of criteria (i) through (v) of Prompt 1. So, if your answer to Prompt 1 earns less than 4 points, any answers you give to Prompt 2 parts (a) and (b) automatically earn 0 points. On the other hand, if your answer to Prompt 1 earned 4 or more points, we score your answers to Prompt 2 Part (a) as follows:

Note that the prompt asks you to compute one probability for each resolution of the uncertainty about the extent of the organization’s competence/discipline/effectiveness as specified in your model. Thus in scoring your answer, we will first inspect your model to see how many of these distinct probabilities your answer should contain. We will mark each of these required probabilities as:

“fully correct” if you give the correct value for the relevant probability, written as a fraction, not as a decimal number, regardless of whether or how that fraction is simplified, and if you provide a marked up diagram that correctly shows how that probability was computed.
“partially correct” if you give the correct value for the relevant probability, written as a fraction, not as a decimal number, regardless of whether or how that fraction is simplified, but you don’t provide a marked up diagram or the marked-up diagram you provide does not show the correct method for computing the probability.
“incorrect” if you do not provide the relevant probability, or you provide it, but the value you provide is incorrect or it is written as a decimal number instead of as a fraction.

When then assign a score to each of the required probabilities as follows:

4 points if it is fully correct.
1 points if it is partially correct.
0 points if it is incorrect.

Finally, your score on Prompt 2 Part (a) is the average of the scores we assign to the required probabilities.

For instance, suppose that the model you wrote in response to Prompt 1 implies that your answer to Prompt 2 Part (a) should have three probabilities. Suppose further that you submit only two of these three, and we score one of the submitted probabilities 4 points and the other 1 point. Then your score on the Prompt 2 Part (a) will be \frac{4 + 1 + 0}{3} = \frac{5}{3} \approx 1.67

Note that all this means that your score on Prompt 2 Part (a), regardless of the number of probabilities required by your model, will range from 4 to 0 points.

Prompt 2 Part (b)

Note first that the prompt asks you to compute one probability for each resolution of the uncertainty about the extent of the organization’s competence/discipline/effectiveness as specified in your model. Thus in scoring your answer, we will first inspect your model to see how many of these distinct probabilities your answer should contain. We will mark each of these required probabilities as:

“fully correct” if you give the correct value for the relevant probability, written as a fraction, not as a decimal number, regardless of whether or how that fraction is simplified, and if you provide a marked up diagram that correctly shows how that probability was computed.
“partially correct” if you give the correct value for the relevant probability, written as a fraction, not as a decimal number, regardless of whether or how that fraction is simplified, but you don’t provide a marked up diagram or the marked-up diagram you provide does not show the correct method for computing the probability.
“incorrect” if you do not provide the relevant probability, or you provide it, but the value you provide is incorrect (whether or however simplified) or it is written as a decimal number instead of as a fraction.

When then assign a score to each of the required probabilities as follows:

4 points if it is fully correct.
1 points if it is partially correct.
0 points if it is incorrect.

Finally, your score on Prompt 2 Part (b) is the average of the scores we assign to the required probabilities.

For instance, suppose that the model you wrote in response to Prompt 1 implies that your answer to Prompt 2 Part (b) should have three probabilities. Suppose further that you submit only two of these three, and we score one of the submitted probabilities 4 points and the other 1 point. Then your score on the Prompt 2 Part (b) will be \frac{4 + 1 + 0}{3} = \frac{5}{3} \approx 1.67

Note that all this means that your score on Prompt 2 Part (b), regardless of the number of probabilities required by your model, will range from 4 to 0 points.

References

Bueno de Mesquita, Ethan. 2010. “Regime Change and Revolutionary Entrepreneurs.” American Political Science Review 104 (3).