Future Research and Conclusions
IN THIS EXPOSITION, I have been essentially interested in the feasibility of a fundamental synthesis, rather than in its robustness to numerical perturbations. Hence, I have left sensitivity analysis for future rounds of work. But it would certainly be interesting to more fully explore the parameter space of the model, charting out its regions of stability.
Numerical Cartography
This numerical cartography could naturally begin with the systematic covariation of the (currently) global variables215 offered as sliders in the Agent_Zero interface. These are as follows:
• Attack rate (stochastic environmental stimulus rate)
• Spatial sampling radius (sometimes referred to advisedly as “vision”)
• Extinction rate
• Memory length
• Action radius
The existing code also allows users to make a number of binary choices:
• Moving average or moving median
• Probability judgments biased by affect, or not.
• Weights exogenous or changing endogenously through strength-scaled homophily
• Homophily based on affect or on probability
• Fight vs. flight.
Agents are already heterogeneous by action thresholds, weights, and learning parameters, for example. But variables and binary settings that are currently global (identical across agents) can also be made to differ across agents. Some agents could use a moving average over a short memory window, while others employ a moving median over a long memory; for some, probability is biased by affect, for others, it is not. Some agents might have high spatial sampling radii, while others are effectively blind.
Tool Set
When one considers the enormous number of possible combinations constructible by covarying these assumptions, it is clear that this book merely scratches the surface of what is constructible from the existing Agent_Zero code. Innumerable explorations and sensitivity analyses can be pursued by adapting the code provided in Appendix III and the full collection of Mathematica and NetLogo programs posted on the Princeton University Press Website. This tool set allows for much further research.
Modular Variants
As noted earlier, the underlying affective, deliberative, and social network components—the submodels of Agent_Zero—are all open for discussion and refinement. This entire development could be seen as a single instance of the myriad models one could assemble from different affective, deliberative, and social constituents, coupled in various ways, as suggested in Table 2. The base Agent_Zero model is the top row.
For instance, one could use the Pearce-Hall model (Pearce and Hall, 1980) rather than Rescorla-Wagner for the affective module. We have ignored anchoring affects in the estimation of probabilities; they could be included in the deliberative module. We explored both fully connected and dynamic network structures. But one could explore many others, including small-world networks (Watts and Strogatz, 1998). Agent_Zero’s overall disposition is the sum of emotional, cognitive, and social components. Future elaborations of the model could explore alternatives to this summation, as in some of the neural network literature.
TABLE 2. Modules for Agent_Zero Variants
Indeed, while affect, probability, and social influence are all dynamic, at any particular time the unadorned Agent_Zero of Parts I and II is, algebraically, a perceptron (Rosenblatt, 1962). That is, the dot product of the input and weight vectors is compared to a threshold.216 One obvious move from the feed-forward neural network literature is to process this raw dot product—the weighted sum of components—running it through a sigmoid function, as in a back-propagation network [see Rumelhardt and McClelland (1987) and Freeman and Skapura (1991)], as suggested in column 4.
One could think of Agent_Zero as a template for a modular social science, where one can swap in and out various affective, deliberative, and social modules.217 And, again, agents could be heterogeneous in these compositions.
Proximity-Dependent Weights
Earlier, I noted that the spatial sample radius employed in the estimation of probability (P) was local, and mathematically independent of the (unbounded) range at which dispositional contagion can, by myriad means, occur. This independence means that Agent 1’s weight on Agent 2 is no different when 1 is inside 2’s sample radius (his “vision,” as it were), than when she is not.
Now, one might wish to explore the consequences if the weight of Agent 1 on Agent 2 is greater when Agent 1’s binary behavior is observed by Agent 1 (occurs within the sampling radius) than when it is not. Since action, A, is either 0 or 1, an obvious way to introduce this would be to generalize the weights as follows: for agents j within i’s sample radius, the new weight 
is given by
where real k 
[0, 1] alters the original weight ωji when A = 1 and does not when A = 0. In the pure dispositional contagion model, k = 1 (which of course stays 1 for either A). We might assign someone high weight based on a cell-phone exchange with her, but when I meet her in person, I see that she is of an unexpected race (or age) and her weight drops. Or a person might have a certain weight based on text exchanges, but when I hear his sophisticated foreign accent, his credibility immediately goes up. In effect, it is a stereotyping extension.218
Neural Deepening
As neuroscience progresses, it may be feasible and productive to increase the modeling resolution, making distributed brain complexes themselves the agents, and our Agent_Zero constituents—affective, deliberative, and social—the emergent phenomena, as it were.219 Agent-based models have generally taken the individual person as the agent. We have introduced affective, cognitive, and social modules. But, we may be able to increase the magnification further, make internal neural complexes themselves the agents, and grow these components. For example, with regard to outright addictions—to tobacco, alcohol, drugs, and foods, for example—the affective module could be deepened to represent the action of relevant neurochemical reward systems. This project appears to be well underway for the dopamine reward system and its role in addiction (e.g., Glimcher, 2011).
Scale-Up
While deepening the agents as the neuroscience warrants, I plan to scale the space and the agent population up dramatically. The feasibility of planetary-scale agent-based modeling is demonstrated in Parker and Epstein (2011). There, the Global Scale Agent Model (GSAM) simulates infectious disease dynamics on a planetary scale, efficiently running 6.5 billion distinct individuals (Parker and Epstein, 2011; Epstein, 2009). But it is easily adapted to the analysis of other large-scale social dynamics. The combination of higher neural resolution and vastly larger scale is an important scientific project.
However, the scale-up, while technically feasible, will need to capture an important phenomenon—namely, that the impact of others’ experience on us often exhibits diminishing marginal returns. In the three-agent version developed here, each agent’s total disposition equals simply her own solo disposition (V + P) plus the sum of others’ weighted solo dispositions. We see no diminishing marginal impact as the number of influencers grows. For two influencers this may be defensible. But when the numbers get larger, unadultered addition probably breaks down. In studies of Latané (1981), for example, impact (assuming unit weights) was found to scale log-linearly in numbers, with slope less than 1. Slovic’s work on psychic numbing (2007) gives even more dramatic scaling examples from such phenomena as famine and genocide. Millions the world over can be riveted by the drama of 33 miners trapped underground (as in Chile 2010), while millions trapped in famine or genocide are treated with virtual indifference. Something tragic happens when we scale up. Empathy is dramatically subadditive. And a large-n model will need to represent that, and perhaps point to remedies for it.
Empiricism
Nicholas Kaldor introduced the term stylized fact into economics, and it is taken as evidence of empirical credibility when economic models are shown to generate stylized facts of economic growth or business cycles, for example. I would make the same sort of claim for Agent_Zero, except that in our case, they have been “stylized dynamics,” of mutual escalation, for example. A somewhat stronger empirical claim might be made for our replication of Latané and Darley’s experiment.
Where data permit, it would be important to attempt the kind of full agent-based computational reconstructions that have been conducted for the Anasazi, for epidemics, and other phenomena (J. M. Epstein, 2006). Where data do not yet permit, theoretical models like Agent_Zero can guide its collection. This is an underappreciated role for models. Frequently, theory precedes and guides data collection (J. M. Epstein, 2008), and I welcome further empirical work on dispositional contagion.
Specific Hypotheses
Models also contribute to empirical activity by furnishing testable hypotheses. Of course, the broadest hypothesis is that Agent_Zero provides a generative explanation of many important phenomena. But, more specific hypotheses have also been tentatively advanced along the way. Among them are these:
1. That the mechanism of threshold imputation can explain the Latané-Darley and related results in social psychology;
2. That affect can amplify probability judgments log-linearly;
3. That the probability of network connection between two agents varies with the product of aggregate affective strength (the sum of affects) and homophily (one minus the absolute affective difference), which offers an alternative to preferential attachment as a mechanism of network formation.
I would welcome experimental or empirical work along all the preceding lines. Meanwhile, I hope that the versatility and extensibility of the Agent_Zero model have been shown. It is an initial step in the direction of a more unified and neurocognitively grounded computational social science. While looking forward to empirical exercises, my claim would be that the simple present model is sufficient to generate important dynamics, that it “gets at” deep things and rings true, perhaps in the way literature does.
Literature
Indeed, as noted in the Foreword, my previous book, Generative Social Science, ends with a challenge: Grow Raskolnikov. Most of our serious dialogues—like Raskolnikov’s own—are with ourselves. And inwardly, I think this is actually what I’ve been working on since throwing down that gauntlet in 2006. Agent_Zero, of course, is not Raskolnikov, but he is recognizable in the same way, and is a fruitful ideal type. Obviously, the scientific merit of Agent_Zero does not depend on the analogy to Dostoevsky’s character. And, as noted, the invocation to “Grow Raskolnikov” was really about growing an internally conflicted agent. Despite that choice being somewhat off-handed, I have enjoyed exploring this parallel and see no harm in discussing it’s appropriateness after all. Like Agent_Zero, Raskolnikov is possessed of (indeed possessed by) distinct and competing modules: (a) an abstract intellectualized one, in which he conceives the murder of his decrepit, but innocent, pawnbroker, (b) an emotional one, in which he experiences the most profound self-loathing over this impulse, and (c) the diffuse influence of the nihilist social movement spreading across educated Russian society (Raskolnikov is a former student) at the time. In his case, the nihilist and intellectual modules prevail over his revulsion, and he commits murder. Recall that in Part III, we conducted an Agent_Zero experiment in which the destructive radius is endogenous, and—with sufficiently poor impulse control—can exceed the stimulus squares. Raskolnikov’s murder radius exceeds the stimulus also: he impulsively kills the pawnbroker’s innocent sister Lizavetta, who happens to appear at the crime scene.220
Obviously, the scientific success of the model does not rest on the success of the literary analogy. But I am gratified that my choice of Raskolnikov was felicitous. It would be very interesting to grow other great figures in literature, or social plot lines, enduring parables that they are!
Data, after all, is the poor man’s literature. But, in all sobriety, an important line of future research will be to compare instantiations of the model—for violence, contagious fear, flight, economic dynamics, jury deliberations, or health behaviors—to available data.
This volume introduces a new theoretical entity, Agent_Zero, whose disposition and behavior depend on affective, deliberative, and social modules. Relevant neuroscience was discussed throughout. Mathematical and agent-based versions were developed. The agent version is explicitly spatial—space is a landscape of stimuli. In many interpretations, yellow patches are “good,” while orange ones are “bad,” or aversive. Agents process the orange stimuli as if they were trials in a conditioning dynamic governed by the (generalized) Rescorla-Wagner model. This produces their affective trajectory V(t). At the same time, they compute the local relative frequency of aversive stimuli and interpret this as the probability that a random patch is an aversive (e.g., enemy) patch. They have memory and in the present version can employ a moving average or moving median over their sampling window. This produces their deliberative trajectory P(t). The emotions and deliberations of others influence each individual’s total disposition, D(t), which is the sum of weighted solo dispositions, taken over the individual’s bi-directional network, where self-weights are unity. This produces what I have dubbed dispositional contagion, as distinct from behavioral imitation.
Interagent weights are endogenized as functions of affective homophily in the model. Each agent has an action threshold, τ. If her total disposition exceeds it, the agent takes the binary action A in question. Succinctly, A = H(D − τ). It is conceptually a very simple model with three parts: affective, deliberative, and social. But it was shown to have considerable generative power. In the course of this exposition, a wide range of interpretations has been developed. I review some here. The first context is the darkest.
Slaughter of Innocents
In one computational parable, Agent_Zero joins a lynch mob (or genocide) despite having no aversion to black people, no evidence of black wrongdoing and no orders to engage in violence. In another, Agent_Zero initiates the lynch mob, not because he is in fact a “leader” in the usual sense, but only because he is the most susceptible to dispositional contagion. If we interpret Agent_Zero as a soldier occupying a foreign country, the stimuli are enemy ambushes and the damage radius is the area (the yellow population) against which Agent_Zero indiscriminately retaliates. This is the My Lai massacre, or the Nazi “collective reprisals,” in which whole villages were annihilated in retaliation for isolated resistance actions.
Overall Picture
The overall picture of Homo sapiens reflected in these interpretations of Agent_Zero is unsettling: Here we have a creature evolved (that is, selected) for high susceptibility to unconscious fear conditioning. Fear (conscious or otherwise) can be acquired rapidly through direct exposure or through observation of fearful others. This primal emotion is moderated by a more recently evolved deliberative module, which, at best, operates suboptimally on incomplete data, and whose risk appraisals are normally biased further by affect itself. Both affective and cognitive modules, moreover, are powerfully influenced by the dispositions of similar—equally limited and unconsciously driven—agents. Is it any wonder that collectivities of interacting agents of this type—the Agent_Zero type—can exhibit mass violence, dysfunctional health behaviors, and financial panic?
Computational Doppelganger
Of course, the central human paradox is precisely that we do see another side: the same Germany that produces Hitler produces Einstein. And, for every ten stories of collective brutality, there are some (fewer than ten, I suspect) stories of collective resistance to it.
Arab Spring
Interpreting orange stimuli as instances of Arab regime corruption and agent actions as the rebellious removal of illegitimate authorities, we generated a caricature of the 2011 Arab Spring. The crucial role of social media in enabling affective homophily to amplify ties and dispositions was demonstrated. Indeed, we constructed a pair of runs in which the same agents, without social media, do not rebel. But, propelled by the dispositional amplification afforded by it, they do. These same stylized facts, of course, characterize a wide range of insurrections, whose empirical reconstruction would be important.
Contagion and Capital flight.
In the preceding examples, the agents’ action is essentially destructive. They wipe out a village, depose a regime, or intern an ethnic group. They fight. But the model easily generates the flight response. One such interpretation posits a landscape of financial or property assets. The agent’s portfolio is the set of assets within his “vision.” Yellow assets are healthy (making acceptable returns). If they suddenly lose value, they turn orange. This results in changes in the agent’s fear (V) that asset values will tumble and changes in his computed probability (P) of such events. If these conspire to elevate disposition above threshold, the agent flees his portfolio, a disposition that can cascade through network effects.
Price Dynamics and Seasonal Cycles
Prices were explicitly introduced into the threshold term. The disposition (or propensity) to consume depended on price in an orthodox fashion. Cycles of supply (as in seasonal variations in strawberry production and transportation costs) were easily generated. Cycles of demand (as in Christmas toy sales) were generated by allowing the landscape of stimuli to oscillate, which drove dispositional cycles. So we did more than simply legislate that demand would oscillate. Affective and dispositional dynamics were intervening forces.
Marketing
Various marketing strategies were shown to have analogues in the mobilization of affective, deliberative, or social components of the agent model. Some further extensions (e.g., Agent_Zero as CEO) were sketched.221
Vaccine Refusal
If the space is a landscape of vaccines, the behavior of interest becomes vaccine refusal, an area rife with emotionality. Given an orange event—an adverse event, or even a report of one—with one vaccine, some agents foreswear all vaccines within a large pharmaceutical radius, while others refuse only a narrow set. As in earlier research (J. M. Epstein et al., 2008), fear itself can, of course, be contagious and generate a large swath of vaccine refusal, far beyond what an empirical risk deliberation would warrant.
Unhealthy Eating
Binge eating is another health interpretation where the space could be coordinatized by carbohydrates (x-axis) and fat (y-axis). Despite computing a high probability of unhealthy effects, the agent—perhaps driven by social network effects—can impulsively consume a large radius of foods, once he is conditioned to associate them with pleasure, holidays, or membership in a group.222 Indeed, as we reviewed, the neuroscience (Kross et al., 2011) suggests that resistance to the group norm can be literally painful.
Aging and Impulse Control
We showed how the destructive radius could be endogenized. Then we made it a function of affect and age, to model the well-known fact that, typically, impulse control is lower in minors than in adults, as recognized in legal distinctions between the two, for example.
Latané-Darley and Zillmann
We replicated the famous Latané-Darley smoke-filled room experiment from social psychology, proposing a new explanatory mechanism—threshold imputation. We also showed the model to be consistent with Zillmann’s experiment, in which connection we ventured another testable hypothesis that affect biases probability in the form 
, which is to say log-linearly in 1 − V.
Posttraumatic Affect Retention
Agent_Zero’s affect can persist undiminished long after any true stimulus has stopped. A variety of simple recognizable parables were generated: bringing a bad mood home from the office, or bringing traumatic fear home from combat or a fire rescue, despite the stimulus episodes ending long before. Passion and reason can move on different time scales. In connection with posttraumatic stress persistence, we explored the effect on the group if even one agent is unable to reset her λ to zero.
We conducted what I believe to be the first in silico lesion study, showing that the excision of one agent’s emotional module had effects not only on their affective trajectory and behavior, but also on their capacity to transmit affect to others and hence had systemic ramifications at the group level.
Three-Phased Process
We used the framework to model a three-phased trial process. Phase 1 was pretrial, in which agents are bombarded with claims of guilt (orange) and presumptions of innocence (yellow) in the public square. They form a V and a P about the defendant before any formal trial begins. Then, if they are chosen as jurors, they are subject to an entirely different stimulus pattern in the courtroom. Their V and P evolve accordingly. Thus far they have still not interacted with other jurors. When, at last, they are sent behind closed doors to deliberate collectively, they reveal their dispositions to convict; network and momentum effects well documented in the literature are then generated. Overall, the verdict under jury deliberation can be entirely different from what any individual juror in isolation would deliver. Counterintuitive effects of a change of venue were discussed.
The Formation and Dynamics of Networks
Affective Homophily and Endogenous Weights
Suffusing all of this are the interagent weights. Initially these weights are exogenous. Then they are endogenized as the product of affective strength (vi + vj) and affective homophily (1 − | vi − vj |). Literature supporting this idea is cited. Then the binary formation of links is modeled as the Heaviside step function of connection weight minus a link threshold. This is an alternative hypothesis to preferential attachment and is yet another testable hypothesis given relevant data. The model can easily accommodate affective, probability, or disposition homophily rather than affective, which was solely explored here.
Multilevel Societies
We outlined how the model could be naturally extended to generate hierarchies in which the actions of Layer_n agents are treated as stimuli by Layer_(n + 1) agents. A number of interpretations—regulatory and peacekeeping organizations—were discussed.
In all the preceding discussion, the yellow activation rate was an exogenous constant set by the user. The concluding extension endows the yellow patches with agency. Harking back to the opening examples of civil violence, we give yellow patches the abilities to (a) endogenously increase their attack frequency in response to occupier destruction and (b) to retaliate on occupiers. We also incorporated a variant on the first of the previously noted extensions, making the occupiers’ destructive radius an increasing function of affect. These alterations generated escalation spirals and permitted the resistance to defeat the occupiers, a general dynamic observed throughout political-military history.
Birth and Intergenerational Transmission
Taking as our inspiration a famous historical passage from Marx’s The 18th Brumaire of Louis Bonaparte, we developed an intergenerational parable in which the parent’s memory—her chronicle—is initially imprinted on the child. But the child leaves home, has new experiences, and eventually “overwrites” the inherited narrative with his own.
We generated all this without any assumption of behavioral imitation. It would appear that a fairly rich social science might be possible without it!
IV.3. TOWARD NEW GENERATIVE FOUNDATIONS
Scientific theory should not aim at realism. It should aim at fruitful idealizations, from which real entities and phenomena can be productively cast as perturbations. There are no ideal gases or frictionless planes. But these limiting cases—which do not occur in nature—turn out to be the productive theoretical entities.223 Not all limiting cases do.224 Agent_Zero is such an idealization.
Agent_Zero vs. Homo Economicus
His or her construction has been my central objective. Recall our opening example. With no negative affect and no relevant evidence, he or she yet perpetrates—indeed initiates—acts of destructive violence. Do real people behave exactly that way? Hopefully, not many. But, if one wished to model participants in genocide, which would be the better limiting case—Agent_Zero or Homo economicus? Which ideal type most naturally accommodates the recent insights of cognitive neuroscience (e.g., indirect fear contagion) or the robustly documented logical confusions, elemental conformity effects, and contagious hysterias observed in Homo sapiens? Certainly, in these contexts, Agent_Zero has some claim to primacy.
It is a simple unified neurocognitively grounded model able to crudely generate central phenomena across the spheres of conflict, economics, health behavior, law, social psychology, and network dynamics. It has what I might call high generative efficiency. The Agent_Zero model itself is minimal, but it generates an extensive space of phenomena. We’ve squeezed a lot out of it, in other words.
Whether this particular agent, or some distant progeny yet to emerge, proves the most enduring, I believe this broad family tree of individuals—each capable of emotional learning, bounded rationality, and social connection — is well worth developing. With agent-based modeling, large numbers of heterogeneous agents in this family can interact directly with one another, generating interdependent dispositional and behavioral trajectories in time and space, which can be compared to data and used to better understand—and perhaps improve—a wide range of important social dynamics. In sum, while it can surely be refined, I offer Agent_Zero as a step toward neurocognitive foundations for generative social science.
215Global variables are the same for all agents.
216This is the input to the Heaviside function first introduced in Part I.
217As noted earlier, the fact that the Agent_Zero formalism can be modular in this technical sense has nothing to do with whether the human brain is “modular,” however one may define the term. The model need not “look like” the thing being modeled, in other words. While a scale model of a bridge does resemble a bridge, I’m not sure it even makes sense to say that a mathematical model “looks like” the thing, or process, being modeled. Hooke’s law “looks” nothing like a spring. It looks like F = −kx. The spring oscillates, the law doesn’t. The equations of general relativity govern, but do not resemble, a galaxy.
218I thank Julia Chelen for this interpretation.
219For a spirited critique of classical emergentism, see J. M. Epstein (2006, Ch. 2).
220One could argue that the second murder is “rational,” in eliminating a witness. But Raskolnikov does not make this calculation; he kills impulsively.
221Brand loyalty was cast as a conditioning phenomenon, and it was suggested that “umbrella branding” exploits stimulus overgeneralization.
222In a more general energy-balance interpretation, the x-axis could be caloric intake; the y-axis could be level of physical activity, and the z-axis could be BMI. Agents located in the lower right are sedentary (low y) and consume high calories (high x). These have high BMI. One wishes to move them to a low-x/high-y lifestyle. But certain paths are clearly not feasible. Morbidly obese sedentary agents cannot immediately increase y vertically and then go left to a low x. They may be physically incapable of immediate vigorous exercise, or their current (e.g., inner-city) environment may preclude it. So, if orange outbursts are opportunities for unhealthy behavior, one wants to present them with a “yellow brick road” to a healthier location. But, with heterogeneous affective and deliberative modules, different social networks, physical opportunities, and budgets, successful trajectories may vary widely across agents. For a variety of simple diet trajectories that could be tailored to heterogeneous individuals, see Hammond and Epstein (2007).
223For an incomparable statement of this Cartesian perspective, see Joseph Epstein’s Introduction to A Discourse on Method, and Other Works (Descartes, 1965; J. Epstein, ed.).
224The physically accurate limiting case for our solar system is heat death. But this would be an unproductive starting point for the study of biology on Earth.