A Methods summary

Agent-Based Social Psychology: From Neurocognitive Processes to Social Data1


Moral Foundation Theory states that groups of different observers may rely on partially dissimilar sets of moral foundations, thereby reaching different moral valuations. The use of functional imaging techniques has revealed a spectrum of cognitive styles with respect to the differential handling of novel or corroborating information that is correlated to political affiliation. Here we characterize the collective behavior of an agent-based model whose inter individual interactions due to information exchange in the form of opinions are in qualitative agreement with experimental neuroscience data. The main conclusion derived connects the existence of diversity in the cognitive strategies and statistics of the sets of moral foundations and suggests that this connection arises from interactions between agents. Thus a simple interacting agent model, whose interactions are in accord with empirical data on conformity and learning processes, presents statistical signatures consistent with moral judgment patterns of conservatives and liberals as obtained by survey studies of social psychology.

agent-based model; opinion dynamics; reinforcement learning; statistical mechanics; neurosociology

I Introduction

The proponents of Moral Foundation Theory (MFT) (35) have identified at least five moral foundations or dimensions that, potentially, are universally present in humans. These dimensions are manifested in different manners, not only across time and cultures, but also within a society. Individuals with different attributions of the relative importance of the dimensions will be led to fundamental misunderstanding of moral motivations of each other. Within the MFT, extensive empirical support (30); (34); (36) has been gathered for the fact that the use of different subsets of moral foundations by groups is significantly correlated with a scale characterizing the group along the political spectrum. The subsets are such that liberals tend to rely more strongly on aspects relating to (a) harm/care and (b) fairness/reciprocity. Conservatives rely on these aspects but not as much. In addition they also regard as important (c) in-group loyalty, (d) authority/respect and (e) purity/sanctity, to a larger extent than liberals (35).

At the scale of individuals, empirical evidence supports that: 1. moral opinions are to a large extent emitted automatically, that is, people, as a first approximation, are intuitionists (31); (32); (33); (34); 2. there is a psychological cost of dissent, with humans trying to attain social conformity modulated by peer pressure (7); (20); (53); (55); 3. conformity is learned from interactions within a social network (40); 4. individual cognitive strategies may differ with respect to the relative sensitivity to learning from novel information as compared to reinforcing habitual responses (6).

Despite the growing body of experimental evidence accumulated over the last decade, explicit connections between this new empirical evidence on individual behavior and social phenomena (or between micromotives and macrobehavior (50)) still are relatively unexplored. Since the work on sociophysics by Galam (24); (25), the statistical mechanics community has already addressed this aggregation problem in social systems (14); (19); (27); (28); (49); (63)2. However, this research has mainly focused on the study of simplified scenarios based on common sense suppositions that result in models that are interesting per se. Some recent works have exemplified a different direction by postulating reasonable inter-individual interactions and trying to predict (26) or explain (9) empirically observed aggregate behavior. We believe that the program of building models explicitly based on the empirical evidence that is now available (23) is worth pursuing.

We do not believe that any stylized model can provide an all encompassing and precisely quantitative description of human nature. Our general goals in this work are instead much more modest and can be stated as follows. Our first goal is to provide a mathematical model that is capable of connecting in the same framework empirical evidence from processes at different scales. We also would like to have a framework that is capable of instigating the formulation of new theoretical and experimental questions. In particular, we propose a model with agents consistent with empirical evidence and study its aggregate behavior by employing the approach and numerical techniques of statistical mechanics. We then show that this aggregate behavior predicts that a well defined feature is expected to be observed in the data we are considering. We then verify the consistency of our predictions and propose a new interpretation to empirical evidence within this framework that can be qualitatively tested against new data sets in the future. We insist that such a general model is only expected to provide qualitative predictions of limited scope and emphasize our belief that a good model should make testable predictions but should not explain too much.

In the following sections we give details on the empirical evidence we consider relevant, introduce our modeling approach, present and discuss the results obtained. A brief summary of methods employed is provided as an appendix.

Ii Empirical evidence for the model

In building our model we have tried to incorporate in a stylized manner empirical evidence. In this section we describe what we believe to be essential empirical observations and which model structures they suggest.

ii.1 Moral theories and the automaticity of moral judgments

Philosophers have struggled with the problem of conceptualizing morality since antiquity. Although philosophical theories tend to be of normative character they can be regarded as a starting point in considering a possible scientific approach for morality as a social phenomenon. Three theories are of particular interest to our discussion: virtue theory, deontology and utilitarianism (11); (37).

According to (13); (37), utilitarianism proposes that moral judgments should be based on the consequences resulting from them. Only actions that maximize social happiness and minimize pain should be taken. In the deontological view only actions that could be universally adopted without violating anyone’s rights should be pursued. Virtue theory takes into account the intrinsic limitations of human nature and states that morality is concerned with maximizing virtues and minimizing vices. Each view of morality presupposes cognitive loads that can be experimentally verified. While utilitarianism and deontology concentrate moral decisions on higher cognitive functions in the prefrontal and sensorial brain regions, virtue theory proposes the coordinated functioning of these areas with others associated to the processing of emotions. Data gathered in the last decade favors a combination of the three views with preponderance of a mode that is closer to virtue theory (33); (41). Actually ample research points in the direction that moral opinions are mostly formed with very few recourse to utilitarian (or consequentialist) reasoning.

Evidence supports that moral violations elicit strong negative responses that activate the socio-emotional structures of the brain (e.g. medial prefrontal cortex and posterior cingulate cortex)3. But emotions are not the only component behind every moral judgment as experimental observation also suggests that these automatic negative responses can be overcome by a more utilitarian mode by recruiting cognitive areas in the prefrontal cortex, in particular, when difficult personal dilemmas with important social consequences are involved (32); (41); (47).

In this work we simplify by only considering the moral grading of statements and not the comparison and subsequent choice between different possibilities and their consequences. Therefore we keep from entering a discussion between deontological or consequentialist (11) moral theories which might guide the modeling of decisions and choices associated to moral dilemmas. We start by supposing as a first approximation that socio-emotional intuitions predominate and that moral grading is in fact automatic.

ii.2 Moral foundations

Human culture and values are markedly diverse. Nevertheless, this diversity seems to emerge from innate universals. Modern research in cultural anthropology (54), primatology (18) and evolutionary psychology (35); (39) suggests that morality may be parsed into a small number of basic intuitions. Haidt and collaborators (30); (35); (37); (36) reviewed the literature to identify five candidates to innate moral intuitions (or foundations) associated to: care, fairness (classified as individualizing foundations), loyalty, authority and purity (binding foundations). This set of innate moral foundations could have coevolved with culture due to adaptive challenges primate populations have been subjected to in their evolutionary history (10); (35). This innateness, however, does not imply moral judgments that are rigid or genetically determined. What is considered to be a virtue or a vice in a given society at a given time depends instead on learning and imitation in a social environment. This plasticity from an initial draft is the key to understand how diversity can be universality-bound (30); (43). In our model we introduce moral foundations as dimensions in an abstract moral state space (for a similar suggestion see (16)). Five dimensional moral vectors live in this space and are animated by an adaptation dynamics elicited by social interactions.

ii.3 Reinforcement Learning

Extensive literature (see (38) and references therein) suggests the existence of a generic machinery for error and conflict processing in humans. This adaptive circuit implements a full-fledged reinforcement learning system. In this system the basal ganglia processes error information provided by the spinal cord, the sensorial cortex and by areas that were traditionally labeled as the limbic system. This error measure is then converted into a dopamine signal that is used to correct responses with the mediation of a strategically connected region known as the Anterior Cingulate Cortex (ACC).

In event related potential (ERP) experiments the processing of social exclusion feelings and social normative conflicts has been associated to error related negativity (ERN) signals with source located in the ACC. This localization has been further confirmed by fMRI (38). Initial activation of the ACC due to conflict has also been associated to subsequent alignment to opinions perceived as preponderant in the social group (40). These new data corroborate classical behavioral experiments on the psychology of conformity conducted by Sherif (53) and Asch (7). Such findings suggest a central role to reinforcement learning in the dynamics of conformity to social norms. The observation of amigdala activation during social conflict (8) together with the known association of the ACC activation when physical pain is involved (20); (55) additionally suggest that disagreement elicits a psychological cost in humans.

Both the automaticity of moral judgments and the psychological cost of disagreement can be represented by using a reinforcement learning model that is well established in computer science (57) and statistical mechanics (21). Within this model a moral judgment is regarded as a classification task. Each agent has an internal moral state . At each time step an agent is chosen and its internal state is updated to minimize the psychological cost. If there is no noise in the communication, this minimization follows a gradient descent dynamics:


where defines the time scale and represents the social cost, namely, the sum of psychological costs incurred by an agent in a given social network.

ii.4 Cognitive styles

A recent experiment (6) has shown evidence that there is a correlation between being a liberal or conservative with respect to social issues and the way novel or corroborating information is used. The experimental setup consists of the measurement of ERPs and concomitant fMRI while participants are exposed to a Go/No-Go task. The subjects first habituate to a frequent “Go” stimulus. In some rare occasions a “No-Go” stimulus appears and a related ERN signal is registered. As expected, a localization algorithm and simultaneous fMRI identify the ACC as a source for the conflict signal. Before the experimental section, the participants are asked to rate their political orientation from for “very liberals” to for “very conservatives”. A negative correlation is then found between political affiliation and the amplitude of the ERN signal. Liberals exhibit more intense conflict related activation of the ACC as compared to habituated response.

Two other recent studies provide further evidence by associating political behavior and genetic differences affecting dopamine receptors known as DRD2 and DRD4 (17); (52). Dopamine is a neurotransmitter directly related, among several other things, to predictive reward systems that modulate reinforcement learning mechanisms (51).

We regard these experiments as suggesting that self-declared liberals are more at ease with novel information and rely less on corroborating information while self-declared conservatives prefer corroboration and are less at ease with novelty. We use the term corroboration to signify “confirming and in accordance to previous opinion”. This new empirical work concurs with ample literature in social sciences which have discussed for decades the relation between cognitive styles and political orientation (2). Whether this cognitive diversity is due to genetic or cultural conditions is beyond our present scope.

We try to capture some aspect of the information conveyed by this class of empirical results by recurring to models of statistical learning (21). We propose that there are different learning styles according to the balance between novelty seeking and corroboration. For that we introduce a parameter that specifies the amplitude ratio between learning corroborating and learning conflicting information and define a learning algorithm interpolating between pure corroboration learning when and pure novelty seeking learning when . In one social interaction we would then have:


where the function


modulates learning of agent by comparing its classification of an input with that issued by a social neighbor . The response of agent is then corrected with direction given by the issue and sign and amplitude dictated by the information provided by agent .

ii.5 Social influence

Classical experimental setups by Sherif (53) and Asch (7) demonstrated that groups influence individual beliefs and decisions. In Sherif’s experiment subjects are placed in a dark room and asked to judge the displacement of a spot of light without knowing that it is actually stationary. The task is repeated a number of rounds with participants either alone or in groups. When in group, individual estimates converge to a group specific norm.

In Asch’s experiment a participant is placed in a room with a group of other people that are, without her knowledge, confederates of the study. She is then presented with two cards. One with a standard vertical line and the other with one vertical line the same length of the standard and two with different lengths. The participant is then asked to identify which of the lines in the second card is most similar to the standard line in the first card, but this is done after all confederates unanimously make the wrong choice. A strong conformist trend is observed, with decreased accuracy of individual judgment.

These experiments are generically consistent with the modern picture of conflict mediated reinforcement learning (40). However, two aspects of these setups require a closer examination: in the first setup participants are anonymous and information ambiguous and in the second information is comparatively objective and subjects largely uncategorized.

Modern social psychology defines three types of social influence (1): informational, normative and referent informational. Informational influence is the predominant mechanism for social influence in the absence of objective evidence and when no group identification is present as in Sherif’s experiment. The expectation of acceptance or punishment by other members in a group leads to normative influence observed in Asch’s experiment. When group membership is salient referent informational influence becomes dominant. In this mode individuals seek to be identified as pertaining to a given group.

To investigate referent informational influence in (1) Sherif’s and Asch’s experiments are repeated with the introduction of salient group membership. It is observed that if a participant regards herself as part of a different group, the conformity effect is greatly diminished.

In our modeling effort we then suppose that referent informational influence is preponderant and, as a starting point, assume the extreme scenario where only in-group conflict leads to conformity effects. We therefore start by considering the case in which agents are circumscribed to social neighborhoods with homogeneous cognitive styles represented by the corroboration/novelty parameter .

ii.6 Social topology

Social networks have received a great deal of attention during the last decade (5). The Internet and social networking sites like Facebook, MySpace or Orkut now make possible to study empirically topological and dynamical properties of social graphs. One of the simplest topological properties that can be defined is the distribution of node degrees . A growing number of studies seems to indicate that many natural networks are well represented by scale-free graphs with the tail of the node distribution given by (5).

To make an informed modeling choice we have searched the literature for networks representing social interactions. We have found some illustrative cases. For instance, the node distribution of a network of phone calls has been found to be scale-free with in (4). The network of sexual contacts has been identified as being scale-free with in (42). By employing a sampling algorithm a power law with has been reported for the Facebook (29), but this estimate relies on a range of degrees spanning only one decade. Other study of entire networks instead supports an exponential node distribution in this case (58). A third study (3) with samples from three social network websites reports scale-free behavior with , and , respectively for Cyworld, MySpace and Orkut.

We have considered empirical evidence and have applied the simple procedure of preferential attachment described by Barabási and Albert (5) to generate scale-free social networks with . We are aware of the fact that clustering properties of networks built in such way will differ from those found in real social networks, however, we have been able to verify that the particular results we present here are sensitive to the degree distribution and qualitatively robust in relation to other topological properties (61).

Iii Agent-based model

iii.1 Combining empirical ingredients

We introduce a model for an interacting society where agents represent individuals that debate moral issues with their social neighbors. In general terms our modeling approach continues a now established line of research on opinion dynamics (14); (27); (60). We however, strongly emphasize that information exchanges and processing, even though stylized, should be explicitly linked to the empirical evidence available.

We start by supposing that the moral state space has dimensions so that moral issues may be parsed into these dimensions. We simplify by assuming only unit vectors. It is certainly possible that the same results we have reached could have been obtained by assuming less (or more) dimensions, however, it would be incompatible with known empirical data that supports the existence of five moral dimensions (34); (35); (36).

We consider that an agent attributes a moral content for an issue that may then be represented by a five component unit vector (issue vector) (60) with and . Here represents the average part of the moral parsing and represents an individual part.

We call the average (normalized) issue the Zeitgeist vector, which can be regarded as describing the cultural environment and providing a symmetry breaking direction in the moral state space. Here we are not to be concerned with the origin of the Zeitgeist4 vector as it results from evolutionary and historical processes taking place in time scales that exceed the scope of our simple model. We further simplify the model by assuming that individual components are such that and are small enough so that they can be disregarded in a first analysis. We are also going to assume that the individual components are not correlated over the social network.

The relevant variables to characterize an agent are suggested by moral foundation theory. For each agent and unavailable to other agents, the internal moral state is encoded in another unit vector (moral vector), also five dimensional, the magnitude of each component representing the weight the -th agent gives to a particular moral foundation. Unit vectors are used to avoid introducing the collateral notion that one agent could be more moral than another.

The automaticity of moral judgment is then represented as a classification task where in an elementary interaction an agent gathers information on the moral classification of her social neighbor on a given issue . This classification is represented by a field given by . Its attributes are its sign and magnitude, indicating respectively whether the issue is considered morally acceptable () or not () and how strongly the agent holds this position ().

At this point we make an additional abstraction leap that leads to a still simpler model: we suppose that a debate is a more complex interaction that involves multiple issues and multiple agents and it works effectively as if the participants were estimating the Zeitgeist vector . Therefore, the effective interaction we are going to consider corresponds to the exchange of fields between neighbors.

We only consider here social influence between similar cognitive styles, namely, agents have homogeneous cognitive styles and interactions are symmetric. To consider the empirical fact that in-group disagreement (or being in the minority) elicits a negative brain response we introduce a measure of the psychological cost of disagreement between socially interacting agents and . It is quantified by , a function of their opinions which depends on a parameter that measures the different treatment of corroborating or novel opinions.

Reinforcement learning can be recast in its off-line version (21) as the process of seeking a minimum in a given cost landscape. Along this line we assume that moral vectors evolve by decreasing the psychological cost under communication through a noisy channel. The social cost is defined by summing over all pairs of interacting agents:


It depends on , the configuration of the society, and on the cultural environment, given by the Zeitgeist vector.

Figure 1: Psychological cost: as a function of and , the angles between , and the Zeitgeist vector where . The potential can be written as if (disagreement) and if (agreement). The figure depicts cases with (left), (center) and (right). The noisy learning dynamics tends to change the making decrease along its gradient. Four peaks represent the cost of maximum disagreement when moral state vectors are opposite and angles are and . Note that when agents agree about the sign of their opinions, the benefit of agreement increases with .

The functional form of the psychological cost must reflect experimental data. The only stylized fact we include is that there are different cognitive styles regarding the different way that novelty and corroborating data is handled. By integrating the modulation function proposed in equation 3 we reach a reasonable choice, by no means unique, that is depicted in figure 1:


The corroboration/novelty parameter () quantifies a cognitive strategy with respect to the difference in treatment of agreement and disagreement as it is suggested by ERP experiments. Our agents are conformists, namely, in the face of disagreeing opinions, the dynamics is such that the social cost is decreased. For (leftmost panel of figure 1) agents are novelty seekers and do not use corroborating opinions since is flat for opinions of the same sign. For (rightmost panel of figure 1) agents seek corroboration and conformity, learning equally in the case of agreement or disagreement.

The techniques of statistical mechanics permit obtaining collective or aggregate emergent phenomena arising from reinforcement learning with the value of the social cost or at least, its average, constituting relevant information to characterize the state of the society with respect to the current Zeitgeist.

iii.2 Incomplete information, statistical mechanics and peer pressure

The incompleteness of the available information about agent moral vectors imposes the use of probabilities in describing the moral state of the society. What is the information available to construct the theory? From the evidence about cognitive styles of persons we have constructed two functions. First, the psychological cost, equation 5, which describes the cost of disagreeing as a function of the opinions of the agents. Second, the social cost, equation 4, is the sum over pairs of interacting agents of the psychological cost. The social cost is about the whole society and results obtained from it will include collective properties arising from the interaction among the agents. It carries two types of information, about the internal space of pair interactions or cognitive level and about the external space, specifically about the geometry of the neighborhood of interactions, or the social level.

A complex system such as a society can be described in many ways. Suppose that we choose to study experimental questions which will have the same answer when the social cost has a given value or a given expected value, averaged over the probability distribution. There might be questions that do not fall into this category. In a physics language, an experimentalist wishes to prepare a system, by deciding on the control of certain parameters, in such a way that repetitions of the experiment will result in compatible answers for a class of questions. There will be other questions that, not resulting in predictable answers, can’t be addressed within that experimental setup. This might be because, at last they are not interesting, or that another experimental design is needed in order to examine them. We concentrate on those questions for which knowing the expected value of the social cost is sufficient. If this cost is not known, then the most tempting thing to do is, by claiming insufficient reason to pick one direction over other, is to assign a uniform distribution for the set of moral vectors. Now, upon learning that the social cost of the society is an important quantity that defines the state, we suppose it known. This simple assumption leads to the introduction of a conjugate variable, the peer pressure scale. Knowledge of one permits calculating the other, although this might be very difficult to do. At any rate, if we ignore both, for a given experimental system, the theory requires that one of them be measured. This is how it goes. We start from a uniform distribution . Suppose that new information is obtained, now the expected value of is known. This is the average with respect to an unknown distribution , which we have to find. Whatever was codified into the prior distribution, it was for a reason. The new distribution will have to include the new information and in some sense, from all those that do, will have to “lie closer” to the prior. Closer means, effectively, that the fewest unwarranted new hypotheses must be introduced. The method to do this exists, and has its roots in Boltzmann, Gibbs, Shannon and Jaynes. See (15) for a modern exposition and justification of the Maximum Entropy method.

The resulting method consists of maximizing the cross entropy between the prior and the posterior distributions, subject to the constraints imposed by the new information and normalization. The constraints are included via the usual method of Lagrange multipliers:


with being the uniform measure on the surface of a sphere in dimensions.

It follows that the probability of configuration is the Boltzmann distribution


The Lagrange multiplier is still free and has to be chosen to impose that the average value of is . The informational content of and is, therefore, the same. Expected values of quantities of interest can be calculated for different values of and of any parameters that enter in , such as . We name the new parameter the peer pressure, since it sets the scale of the effect of social cost, and measures the inverse level of noise in the communication channel.

Iv Data on moral foundations

Data consisted of five dimensional score vectors with components in the interval representing the relevance attributed to each moral foundation. Each vector was also labeled by the subject’s self-declared political affiliation from p.a. (very liberal) to p.a.= (very conservative)(30); (36).

Scores were extracted from Moral Foundations Questionnaires (MFQ30)5 taken by US citizens. These questionnaires combine Studies 1 and 2 reported in (30) and are composed by two parts each with sentences ( for each foundation) plus one verification sentence.

In the first part subjects are asked the question: “When you decide whether something is right or wrong, to what extent are the following considerations relevant to your thinking?”. Answers are given by scaling sentences of moral content from “not at all relevant” (score) to “extremely relevant” (score). In the second part subjects scale sentences of a moral content from “strongly disagree”(score) to “strongly agree” (score). A moral vector component is then the average of scores corresponding to a particular moral foundation. Moral vectors are obtained by normalizing score vectors.

Figure 2: The transition line separates phases with zero (below the line) and non zero average overlap with the vector (). The phase transition is continuous. Symbols represent average and dispersion for simulation runs of a system with scale-free Barabási-Albert topologies. The full line represents a fit to the transition border line , with constant. This can be seen more clearly in the inset. Dashed lines represent confidence intervals for a regression.

V Results

We describe the aggregate behavior of the model and compare it to the aggregate behavior extracted from MFQ30 questionnaires. By introducing appropriate order parameters we can compare both systems, the set of subjects and the agents, in a semantic free manner. The correlation of political affiliation and different cognitive styles is established by first showing that different cognitive styles are associated to different distributions of moral values in the agent model and noticing that different sets of moral values are associated to different political affiliations in the MFQ30 data. A group of socially interacting members with a diversity of cognitive styles will therefore present a political spectrum. Groups of conservative agents show larger in-group coherence while groups of liberal agents adapt faster to changes in the issues under discussion.

Figure 3: Histograms for the effective dimension for p.a.= to . Histograms for simulations at and different values of are depicted as dashed lines for comparison. Simulations have been performed with a scale-free social network of size . Results are qualitatively robust to changes in the lattice topology and system size.

We now discuss the statistical signatures that can be used to characterize the effective number of moral foundations of an agent. We compare them with equivalent signatures derived from the MFQ30 data.

Our main concern is the difference in the distribution of weights attributed to moral foundations by self-declared liberals and conservatives. Numerical simulation techniques, briefly discussed in the appendix, show that the model can have two qualitatively different regimes depending on the parameters and (figure 2). For low and low , the system is in a disordered state characterized by random correlations between the moral state vectors of the agents. Increasing either or , a transition line can be crossed into a partially ordered society. Now the agents are correlated to a symmetry breaking direction , the Zeitgeist vector, which can be regarded as describing the cultural environment. The average agent is parallel to . Now we reorient , by rotating the frame of reference, so that its components are equal (e.g. each), explicitly assuming the equivalence of all moral dimensions. Note that opinions are rotation invariant and rotating makes no numerical difference. But it does foster interpretation, since a measure of the effective number of moral foundations of agent can be defined as proportional to the sum over the moral dimensions , of the agents moral weights:


the overlap between the moral vector and , ranging from to . An agent with all moral dimensions equally important has . Smaller values mean it relies on a reduced subset of moral dimensions. From the survey data, we extract, for each person a similar measure of their number of moral dimensions.

Figure 4: By matching the mean average dimension, the relationship between the cognitive strategy parameter and the political affiliation is identified for to . The dashed line represents the case depicted in figure 3. Simulations were performed with a scale-free social network of size . Results are qualitatively robust to changes in the lattice topology and system size.

Our aim is to compare the statistics of from the data and from the model. Figure 3 compares histograms of as obtained from the data and as generated by the model, for on a scale-free social network. We have done several studies including different versions of the model. The conclusions we present, as far as the temptation of detailed quantitative confrontation with the data is tamed, are independent of the different variants of the model. We have only considered symmetric and homogeneous interactions which allows for the use of a single throughout the social network. In all simulations presented in this paper the social neighborhood was represented by a scale-free random graph generated by a Barabási-Albert model (45) with branching rate . We have also simulated a society subscribed to a two dimensional square lattice with nearest neighbor interactions. While this neighborhood seems too artificial, the results were qualitatively similar to those reported in this paper. Results within scale-free topologies, however, show the best agreement with data as far as overlap histograms depicted in figure 3a are concerned.

Agents have no political affiliation and persons do not declare their cognitive strategy . However, histograms permit identifying a political affiliation with a cognitive strategy. Figure 4 was prepared by calculating for each p.a. class of the data and then finding, for each given fixed , the parameter that matches ( Metropolis runs, ). Figure 4 also shows that the connection between the corroboration/novelty parameter and political affiliation is qualitatively robust for a reasonably wide range of .

Vi Discussion

The observations of the last section permit establishing the following link: political affiliations are partially derived from subsets of moral foundations, which arise collectively from distinct cognitive strategies. We conclude that the link described in the literature connecting political affiliation to cognitive style (30); (35) arises as a consequence of social interactions.

As the order-disorder border line (figure 2) is approached from the ordered phase, the overlap with decreases, vanishing at the phase boundary. The best resemblance of the data and simulations occurs by identifying conservatives with agents far into the ordered phase and liberals with agents near the transition line but still in the ordered phase. Order and disorder refer to long range correlations and should not be attached to judgments of value.

We can go beyond the average number of moral foundations and make a prediction, based on the behavior of the agent model, about the width of the histograms. They decrease with increasing and the data shows that they decrease also with conservative tendency. The same identification: novelty seeking behavior to liberals, corroboration to conservatives, is again seen to arise as a consequence of collective behavior.

Order-disorder transitions can be driven by changing the peer pressure. Even without crossing the phase boundary, the model can be used to understand collective swings from left to right, as external conditions impose increased levels of peer pressure arising from the perception of threats. The reverse swing can also be understood when conditions demand higher adaptability to new challenges. We claim that with respect to moral issues, despite the differences in opinion derived from differential reliance on moral foundations, both conservatives and liberals are on the same side of the border. Other scenarios are discernible from the phase diagram. In an application outside the realm of morality, by looking at opinions on issues for which peer pressure might be lower, a group of large agents, relying on corroboration, could be found in a disordered phase and seem on this set of issues, to be liberal.

This theory is semantically neutral. Evolutionary considerations should be used to dress the theory with semantics and to understand why certain foundations of morality have emerged before others and why they are different, thus breaking the remaining symmetry between the five dimensions. Our model cannot claim to shed light on the different nature of the different moral foundations. It just states that based on differential treatment of novel and corroborating information, on conformity seeking behavior and on social interactions, populations will present collective statistically different moral valuations in a way that can be quantitatively described.

We believe that this work may create a number of opportunities for future research. Firstly it is highly desirable to test the model against new data sets. To give three illustrative examples: 1. in (52) a connection is made between the structure of social networks during adolescence and political preferences in adulthood; 2. in (59) it is found that the opinion of a typical member of a virtual social network is influenced by about of their neighbors; 3. (56) makes an empirical analysis of the voting patterns of US federal judge panels finding correlations between the political affiliation of the majority and the decisions reached. Our view is that the model we have proposed might have something to say about what sort of patterns are expected to be seen in each one of these examples.

We suggest that a social cost can be defined and that its mean value is directly associated to a parameter we have identified as the “peer pressure”. We regard the measurement of peer pressure as a relevant open problem suggested by our modeling effort. Finally, the model also has some consequences that could be empirically verified, for example: 1. peer pressure acts as a control parameter that if increased can transform a group regarded as liberal into a conservative group. The reverse also being true; 2. a liberal group would adapt to changes in the environment faster than a conservative group but would not reach consensus easily.

We consider, however, as the most important contribution of this work to emphasize a particular methodological approach to the social sciences. From the description of how individuals react to incoming information obtained from social psychology empirical methods and neurocognitive data, we built an interacting model. Statistical mechanics leads to aggregated predictions which are tested against extensive data sets with partial information about populations. The exchange of information and the learning it elicits, induce collective emergent properties in the society not to be found in the individual. Presumably it may be useful to understand how cultural divides, such as those between conservatives and liberals, arise partly as consequences of diversity of neurocognitive mechanisms.


Experimental data furnished by Jonathan Haidt, whom we thank for kindly permitting us to have access to the data. This work received support from FAPESP and CNPq under grant 550981/07-1.

Appendix A Methods summary

a.1 Metropolis sampling

We assume that the model society is represented at micro-scales by continuous opinions and that the system statistics can be described at intermediary time scales by a Boltzmann distribution:


with being edges of a social graph and is the psychological cost given by (5). The statistics for the overlaps , depicted in figure 3a, can be obtained by sampling from (9). This has been done by employing a classical Metropolis sampling technique (46). The C code employed is provided as an ancillary file to this document.

We choose a random Zeitgeist vector . The distribution (9) is symmetric in relation to sign changes in the components of this vector. To deal with this degeneracy all simulations are started with moral vectors aligned to the direction . More realistic information exchange dynamics to be published elsewhere shows that the system auto-organizes into the same macrostates obtained by this simplified procedure.

a.2 Wang-Landau algorithm

While Metropolis-like algorithms sample from the distribution and collect data at a single point in the phase diagram, there is another class of algorithms which permit collecting information that will allow to obtain results for a set of parameter values. The Wang-Landau algorithm (62), belongs to this second class. The main theme is to collect information about the density of states, which in this case is peer pressure () independent and then to propagate to different values of , by re-weighting via the Boltzmann factor. This is done for a particular value of the novelty/corroboration parameter . The density depends on and so this procedure has to be repeated for a set of values. The C code employed is provided as an ancillary file to this document.

The transition line in figure 2 was obtained by Wang-Landau sampling of a system with Hamiltonian at temperature by finding numerically the maximum of the specific heat for fixed .

a.3 Empirical histograms

Data consisted of moral vectors with components related to five Moral Foundations in the interval extracted from a specially designed the MFQ30 questionnaire(30). Each vector was labeled by the subject’s self-declared political affiliation (from p.a. to ). We first calculated normalized moral vectors and, by defining the vector as the average vector within the conservative (p.a.) and very conservative (p.a.) classes, we have calculated histograms for the effective number of moral dimensions (depicted in figure 3a).

p.a. score n p.a. label
1 very liberal
2 liberal
3 slightly liberal
4 moderate
5 slightly conservative
6 conservative
7 very conservative
6+7 conservative


  1. Preprint of an article submitted for consideration in ACS 2011 World Scientific Publishing Company http://www.worldscinet.com/acs/
  2. That methods from physics can be used in sociology is not particularly surprising, as these methods were actually brought to physics in the 19th century by James Clerk Maxwell when he was inspired by the historian Henry Buckle’s account of Adolphe Quetelet’s statistical approach (48) to social science ((12) p. 438).
  3. For a discussion of the emotional components of moral intuitions and their neural substrates see (44) and (64), see (33); (31) for fMRI evidence and (34) for psychological tests.
  4. For an essay on the role of the Zeitgeist in historical explanation see (22).
  5. Available at moralfoundations.org (accessed on February 7, 2011).
  6. footnotetext: Error bars represent symmetrized bootstrap confidence intervals.
  7. footnotetext: denotes the median of the overlaps .
  8. footnotetext: We consider the classes “conservative” and “very conservative” together as their statistical moments, shown in the table above, are indistinguishable.


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