Disruption of Social Orders in Societal Transitions as Affective Control of Uncertainty

Bayesian Affect Control Theory Fundamentals

Affect Control Theory can be used to simulate an interaction given a set of identity and behavior labels. The interaction modeled by ACT is referred to as connotative, as it gives the affective meanings of events. In BayesACT, the restriction of fixed identity and behavior labels is lifted, and sentiment variance is also taken into account (Hoey et al., 2016, 2021; Schröder et al., 2016). Consequently, BayesACT must model the identities and behaviors denotatively as well as connotatively, as it must maintain a distribution over them representing the agent’s belief that these are the current identities and behaviors at play. The denotative component models the linguistic labels representing the state of the world (e.g., the identity of “doctor” or “nurse,” or the behavior of “advising” or “ignoring”), while the connotative component is like ACT but includes sentiment distributions. BayesACT can be thought of as maintaining a frame that defines the situation in terms of a set of propositions and their associated sentiments. These frames are also referred to as state spaces: an enumeration of all possible values that can be taken on. For example, the denotative state space over identities consists of all known labels for identities (e.g., “nurse,” “doctor,” and “administrator”). The connotative state space is the real-valued space of evaluation, potency and activity as in ACT.

The denotative component can encode constraints on the denotative state. Such constraints constitute a toolkit of social norms, rules, expectations of behavior, or other aspects of the context, and may include denotative stereotypes (e.g., associations between characteristics of people and expected behaviors). Actions may also be constrained in this way, leading to hard-coded policies of action sometimes referred to as repertoires, patterns of behaviors that are pointed to and labeled as narratives, and sets of repertoires and narratives that form institutions (MacKinnon & Heise, 2010; Vaisey & Valentino, 2018). For example, it may be connotatively coherent for a “coal miner” to “work in a coal mine,” but this may not be possible because the mine was shut down for being too polluting. Such constraints may be uncertain, and thus may be modeled with a probability function. Overall, BayesACT generalizes ACT by explicitly representing the distribution over sentiments in a two-level partially observable Markov decision process (Åström, 1965).

In the BayesACT model, there are thus two levels of representation and control. One, connotative level represents the sentiments associated with a given identity-behavior event. A connotative action is explicitly encoded as the behavior sentiment. The other, denotative level represents the actual event itself, including the identity and behavior labels. Denotative actions are encoded as behavior labels. The somatic transform is a probabilistic function that measures the congruence between denotative and connotative interpretation as a probability distribution over labels and a density function in EPA space, respectively (MacKinnon & Hoey, 2021). The somatic transform allows BayesACT to operate as a dual-process model (Hoey, 2021; Hoey et al., 2021; Vaisey, 2009) in which actions are optimized for both connotative coherence and denotative objectives (e.g., goals). It has an equivalence in non-Bayesian ACT as a sentiment dictionary, which defines symbolic boundaries (Vaisey & Valentino, 2018), but is fixed and non-probabilistic.

At any time, BayesACT maintains a probability distribution over both the connotative space and the denotative space. One can imagine this distribution in the connotative space as a continuous function in three dimensions, higher values of which represent more likely connotative meanings for the current state. In the denotative space, the distribution is a multinomial over possible labels (e.g., a person in a hospital setting who is unknown to you may be identified as a “doctor” or an “intern” with nearly equal probability, as a “nurse” with a smaller probability, or as a “patient” with a very small probability, which would be represented as a set of four numbers that sum to 1, e.g., [0.45,0.34,0.01,0.2]). These probability distributions can be characterized by how dispersed they are. A very dispersed distribution is one that is spread evenly over the state space. The opposite of this is a precise distribution, in which the probability mass is concentrated on only a few denotative options, or in a small region of the connotative space. One can think of these as the variance in the prior and posterior distributions over connotative and denotative state spaces (frames). Figure 1a shows example distributions in sentiment space for one dimension for these four example identities, as well as the denotative distribution as a bar chart in Figure 1b and the resulting connotative mixture distribution in Figure 1c.OPEN IN VIEWER

In the BayesACT model, one denotative action is randomly selected from the denotative probability distribution over behaviors for enactment in the following event. Thus, the action selected is a product of denotative and connotative reasoning and there are two control mechanisms used to select actions that are intertwined. As the connotative and denotative spaces have different dynamics (predictor functions), it rests on the relative strengths of the predictions in each, coupled with the relative strength of the somatic transform to determine which of these systems will carry more “weight” in the determination of action. Thus, the two control mechanisms are tightly connected (inextricable), and complementary in that one takes over when the other fails, and the control policy associated with each optimizes different objective functions (MacKinnon & Hoey, 2021). While the denotative state optimizes over preferences, the connotative policy optimizes shared emotional meanings. The principle of complementarity states that both are necessary for action to take place. While denotative framings guide decision-theoretically rational decision-making processes, connotative meanings frame the denotative process, giving rise to deep emotional constraints on the possible actions that are considered.

Management of Uncertainty in Bayesian Affect Control Theory

There are three primary elements in the BayesACT model that represent uncertainty: the dispersion of the denotative distribution, the dispersion of the connotative distribution, and the dispersion of the connection between the two. First, consider the denotative model. The dispersion in an actor’s model is directly related to its resource bound (its ability to carry out computations) and to the complexity of the environment. Environments with many other actors attempting to cooperate are highly complex, and therefore contain much more ambiguity arising from the actor’s inability to model the large quantity of potential configurations that its known environment could be in. An actor can either accept the increased ambiguity, and accept dealing with an invalid world (Kahneman & Klein, 2009), ² or can allocate cognitive resources to the situation. This latter option corresponds to gaining expertise in the domain, and so the actor would be labeled an “expert,” and the situation would become more valid from their perspective (but maybe not from others in the same environment). Thus, low-complexity or high-resource environments are considered valid, while high-complexity or low-resource environments are considered invalid (Kahneman & Klein, 2009). The validity of the denotative model is represented by a parameter. δ ^ ³ In a simple two-state situation (e.g., two labels in a vector [“nurse,” and “doctor”]), the denotative distribution might be invalid (e.g., a distribution over the same vector space [ δ ^ , 1 − δ ^ ] = [ 0.5 , 0.5 ] , so there is great uncertainty about which label should be applied to this person), or valid (e.g., [ δ ^ , 1 − δ ^ ] = [ 0.99 , 0.01 ] , so the person is almost certainly a “nurse,” not a “doctor”).

The connotative model’s precision is afforded by the strength of the affect control principle, which states that persons will behave in ways so as to increase coherence between their feelings about entities out-of-context (fundamental sentiments) and in-context (transient impressions). The strength of the affect control principle is represented by a parameter ( α ^ ) , which was arbitrary in ACT (Heise, 2007), but obtains scale through comparison with validity (denotative precision) and the strength of the somatic transform ( γ ^ ) , (Hoey et al., 2021). The parameter γ ^ measures degree of inextricability of denotative and connotative meaning spaces, and makes up the third element in the representation of uncertainty, which we will here refer to as dependence; that is, the degree to which connotative meanings depend on denotative meanings, and vice versa. Agents in more diverse environments will have weaker somatic transforms ( smaller γ ^ ) , and weaker affect control principles ( smaller α ^ ) , as they are confronted with a greater diversity of different identities and behaviors.

Imagine you are in a hospital and you see someone wearing a white coat. The validity is how certain you are that this is, in fact, a “doctor” (not an “intern”). If it is your family doctor, this certainty may be very high (uncertainty in the label is very low). If it is someone you don’t know, your certainty may be lower. Given that this person is a doctor, your uncertainty in the sentiments about the doctor in EPA space is given by the dependence parameter. The lower this parameter, the less sure you are about how your culture feels about doctors. Perhaps you live in a place where there are “good” doctors and “bad” doctors in roughly equal proportions. Your certainty about how to interpret this doctor will be much lower than if you live in a place where almost all doctors are considered “good” by society at large. Finally, the coherence of the situation is how certain you are that this doctor, who is good (say), will behave in a way that is consistent with his and your identities.

To sum up, the three elements are

validity: the precision of the denotative model (determines the denotative distribution, includes denotative evidence, parameter δ ^ );

Now, consider how these three elements will trade off against each other. The distribution over both connotative and denotative state spaces is the combination of these three representations of uncertainty. One can think of these precisions as the strength of constraints in both connotative and denotative levels, and between them. In BayesACT, a strong set of constraints at one level will mean that the elements of the state (denotative or connotative) connected to those constraints will have a larger influence and be more well defined. Thus, a precise affect control principle means that transient impressions and fundamental sentiments are strongly constrained to be close to one another. If the other distributions (to the denotative state and associated denotative evidence) are kept the same, then an increase in affect control precision will strengthen associations of sentiment to their culturally accepted prescriptions as described by ACT, probabilistically re-evaluating denotative evidence if necessary. On the other hand, a precise denotative distribution will be skewed in one direction or the other, and will more heavily shift the connotative meanings to be in line with one denotative interpretation of the state.

For example, in our hospital setting, suppose you see a woman in white lab coat. There are denotative constraints (with strength δ ^ ) related to who is likely to be in a hospital (nurses, doctors, patients and interns), and who is likely to be wearing a white lab coat (doctors and scientists). These constraints may be satisfied (the person in the lab coat giving orders is a doctor), or not (the person is actually an intern). There are also connotative constraints (with strength α ^ ) that indicate what types of actions are expected by these identities (people will be deferential to doctors because they are good, and doctors will direct others because they are powerful, whereas other workers may take direction and do not require as much deference). Further, stereotypes based on physical traits (e.g., gender) may skew expectations denotatively (the posterior probability that the woman in the white coat is a nurse may be higher due to a gender stereotype), or connotatively (towards less deference culturally associated with the fixed and observable gender characteristics). Finally, denotative and connotative factors are constrained to be consistent through the somatic transform (with strength given by γ ^ ), (e.g., doctors are expected to be more powerful than nurses). While the woman in the white coat may be estimated to be a nurse denotatively, she may be estimated to be a doctor connotatively because she is ordering people around. These two interpretations would conflict to a degree given by γ ^ . All three of these elements combine to form a final determination, in which the denotative identity of the person in the lab coat may be more weighted towards doctor than nurse. In situations of conflict, the determination can still be made, although the final distribution may be much more dispersed due to the disagreement.

The three aspects of uncertainty we have been discussing are modeled with parameters in BayesACT ( δ ^ , α ^ and γ ^ ) that control the amount of dispersion (variance) in distributions of connotative and denotative states. Take a moment to consider what these dispersions really mean. Using the “artificial intelligence” method of seeing if we can build something that works like a human, these variances are the degree of uncertainty in the agent’s “mind.” However, that degree of uncertainty is directly predicated on the degree of uncertainty in this agent’s ecological niche, and vice versa. In this sense, we can equate individual level variance with cultural level variance, but only if there is sufficient coordination amongst the agents that share the culture. Without this coordination (e.g., everyone working on a joint project), the mapping becomes much weaker.

The analysis of the three uncertainty parameters proceeds by first establishing that they cannot all three be small (very dispersed). Should this happen, both the connotative and denotative distributions of each agent in the group, and therefore in the group as a whole, are guaranteed to also be very dispersed. Why is this a problem? Recall that both connotative and denotative elements in BayesACT contain a representation of action, and can be used to derive a policy of action that an agent is consciously aware of. For an agent to be motivated to take an action according to this policy, the distribution over actions must be sufficiently precise. The precision of the distribution over connotative actions then provides the impetus to act. This fits well with neuroscientific evidence that the strength of emotional appraisals (what we call the connotative state) are instrumental in catalyzing action (Damasio, 1994; Gilead et al., 2021). Therefore, if all agents in a group have very dispersed connotative distributions, all will be less certain of risk, and none will be motivated to act, leading to a dysfunctional group. ⁵ Can all these dispersions be very small (high precision)? The answer is unfortunately “no,” because the posterior distributions have to be located in somewhat the same region of the state space in order to “find” each other. Using the notion of the three sets of constraints above, the system is over-constrained, which often leads to the non-existence (or great difficulty of finding) a solution. Therefore, we see that only one or two of these constraints can be strong at one time.

Finally, we can postulate that only one of these constraints can be strong at a time. Suppose the denotative distribution was very precise, then fundamental sentiments and transient impressions would be required to be such that they agreed with this denotative interpretation, but could not be so if they were too constrained to either lie near each other. An allegorical presentation of this matching problem is that of a triangular enclosure with a mass at the center connected by a spring of a different stiffness to each corner, as shown in Figure 2.

The spring connecting the mass to each corner has a stiffness which is proportional to the precision of the corresponding uncertainty management element (coherence, validity, or dependence). That is, a stiffer spring translates to a more precise (= less dispersed) element. When one of these forces is relaxed (e.g., denotative uncertainty is increased, validity is decreased), the other “takes up the slack” and naturally contracts (e.g., the affect control principle is strengthened, and connotative coherence is increased in importance). To summarize the argument at this point, an increase in one form of uncertainty will force a shift in the balance of how the other forms of uncertainty are managed. In the next section, we will argue that this mechanism can explain emotionalization and polarization of social conflict in times of societal transitions.OPEN IN VIEWER

Rationale of the Simulations

The scenario is an interaction between an environmentalist and a coal miner. Substituting coal-based electricity generation with renewable and emission-free solar energy is a major requirement in order to stay within the bounds of the carbon budget of 1.5 degree Celsius rise of average global surface temperatures as per the Paris agreement on climate change. However, the debate about phasing out coal as a source of energy is often far from factual and rational, and is subject to much political polarization. The goal of our simulations is to show how such polarization can arise from identity-verification mechanisms as theorized in Bayesian affect control theory, but that the extent to which conflict occurs in such interactions will depend on the configuration of uncertainty-management processes of the involved agents.

Formally, we are engaging in a computational experiment, where the scenarios differ in the configuration of two of the agents’ uncertainty parameters (incoherence of interactions α , and independence on affective meanings γ), while the denotative invalidity δ, and the identity EPA meanings and impression-change dynamics (parameters typically varied in affect-control theory research) are the same across the simulations. ¹⁰ We study the emerging behavior dynamics in the BayesACT simulation and interpret them in terms of our narrative of societal change due to climate change mitigation policies.

Data Sources and Setup

There are four simulations in total. In each case there are two agents called Hank and Tom, who start out with two identities with equal probability of p = .5. One of the identities is that of a citizen for both agents, to implement in the simulation the French Republican ideal that every person regardless of what their other identities may be is a citoyen capable and willing to engage in democratic and rational debates. However, Hank and Tom differ in their other identity, to implement in the simulation the possibility of contestation and conflict. Hank sees himself as an environmentalist and Tom as a culprit, whom he holds to some extent accountable for the negative effects of climate change. Conversely, Tom sees himself as a coal miner and Hank as a prosecutor, who illegitimately makes moral judgments about his (Tom’s) lifestyle.

For the following simulations, the impression change dynamics are based on the USA 1978 study (Schneider, 2006), while the identity and behavior sentiments (means only as variances are set using γ—see below) are taken from the USA 2015 study (Smith-Lovin et al., 2016). Both are samples of Americans at large universities. To avoid institutionally awkward simulation outcomes, which often occur in affect control theory models without institutional/denotative filters, we manually restricted the list of identities and behaviors to a set we intuited might reasonably occur in our simulated scenario. Mostly, this meant picking relevant occupational identities and behaviors, but also a few which might make sense in a more metaphorical way. For example, Tom viewing Hank as a prosecutor is not institutionally viable in a strict sense, but we think this choice of identity expresses the feeling of being morally “under siege” experienced by some people whose lifestyles are criticized in environmental discourse. We selected a subset of 116 identities and 29 behaviors from the main study sample by manually filtering the dictionary and only keeping words that could be logically applied to the situation at hand. ⁷

In the following we show two simulations. In both, we set δ = 0.1, meaning that each behavior passed from one agent to other is corrupted by Gaussian noise with a standard deviation (SD) of 0.1 in EPA space. This may or may not cause a change in the denotative label (likely not). In the first, we show agents who have aligned parameters: they match in size (both agents use α = 0.1, γ = 0.15). ⁸ In the second simulation, we use parameters that are mis-aligned: one is larger (around 0.1) while the other is smaller (around 0.01), and which is which different between the two agents (so one is α = 0.01 γ = 0.25 while the other is α = 0.5 γ = 0.01).