A Computational Model of Rule-Governed Behavior in the Development and Persistence of Parental Alienation

## Abstract

Abstract

Parental alienation (PA) presents a significant challenge for clinical and legal systems, which struggle to distinguish a child's justified rejection of a parent from manipulated animosity. This paper proposes the first agent-based computational model of PA, grounded in established behavioral science. We synthesize four theoretical pillars: (1) the precedent of agent-based modeling in child welfare (Hu & Puddy, 2011); (2) Relational Frame Theory's concept of the Rule-Based Insensitivity Effect (RBIE) as the core psychological mechanism (Harte et al., 2020; Kissi et al., 2020); (3) the clinical concept of belief perseverance to model the apparent irreversibility of severe alienation (Anderson, Lepper, & Ross, 1980); and (4) a concrete taxonomy of observable alienating and alienated behaviors drawn from clinical literature (Baker, 2007; Gardner, 1985). Our model simulates how a parent's alienating behaviors (e.g., denigration, limiting contact) can install verbal rules in a child that override the child's direct, positive experiences with a target parent, leading to the emergence of specific alienated behaviors in the child (e.g., a campaign of denigration, lack of ambivalence). We then propose a series of computational experiments to test the conditions under which a child's alienated beliefs can be reversed, including scenarios involving continued exposure and court-ordered equal custody. The model provides a rigorous, falsifiable framework for understanding the dynamics of PA and offers a potential tool for educating legal and mental health professionals.

1. Introduction

The phenomenon of a child's rejection of a parent following a high-conflict separation is a complex and painful issue confronting legal and clinical systems worldwide. A central diagnostic and jurisprudential challenge lies in differentiating justified estrangement, where a child's animosity is a reasonable response to a parent's behavior, from parental alienation (PA), where the animosity is the result of psychological manipulation by the other parent (Baker, 2014). The consequences of misidentification are severe, potentially leading courts to leave a child in a harmful, manipulative environment or, conversely, to force contact with a genuinely abusive parent.

Current diagnostic methods rely on post-hoc analysis of observed behaviors and self-reports, which are often unreliable in a high-conflict, litigious context. What is needed is a process-oriented, explanatory model that can simulate the dynamics of how alienation develops over time and, critically, what happens when various interventions are applied.

This paper introduces the first such model, grounded in four pillars of established science:

Methodological Precedent: Agent-Based Modeling (ABM) has been successfully used to simulate complex social dynamics in child welfare (Hu & Puddy, 2011).
Psychological Mechanism: The Rule-Based Insensitivity Effect (RBIE), a concept from Relational Frame Theory (RFT), provides a powerful explanation for how verbal rules from one parent can make a child insensitive to their direct experiences with the other parent (Harte et al., 2020; Kissi et al., 2020).
Clinical Persistence: The psychological principle of Belief Perseverance explains the locked-in or apparently irreversible nature of severe alienation, where beliefs persist even when contradictory evidence is presented (Anderson et al., 1980).
Behavioral Grounding: The model is explicitly tied to a taxonomy of observable alienating behaviors by parents and alienated behaviors exhibited by children, as identified in the clinical literature (Baker, 2007; Gardner, 1985).

By integrating these pillars into a computational framework, we can move beyond static observation to simulate the causal chain from alienating acts to a child's internal belief state and, finally, to the child's observable behaviors. This allows us to ask the questions that matter most to families and courts: What is the threshold for a belief to become resistant to change? And can a child recover once that threshold is crossed, especially under realistic conditions of continued exposure to the alienating parent?

2. Theoretical Framework

Our model stands on the shoulders of four established areas of scientific inquiry.

2.1 Pillar 1: Agent-Based Modeling in Child Welfare

Agent-Based Modeling (ABM) is a computational method that allows researchers to create virtual "agents" (e.g., individuals) with defined attributes and behavioral rules, and then simulate how their interactions give rise to emergent, macro-level patterns (Jackson, 2017). This bottom-up approach is well suited for studying complex systems where feedback loops and individual heterogeneity are important.

A direct methodological precedent exists in the work of Hu and Puddy (2011), who developed a cognitive agent-based simulation of child maltreatment dynamics. Their model used agents representing parents and children with state variables including parenting stress, parental efficacy, and the theory of planned behavior, and incorporated causality relationships and feedback loops from different factors in the social ecology. The success of this approach in modeling the dynamics of child maltreatment validates the use of ABM for the closely related phenomenon of parental alienation. Our work follows this precedent, substituting parental stress with rule-governed behavior as the primary causal variable driving the child's trajectory.

2.2 Pillar 2: The Rule-Based Insensitivity Effect (RBIE)

Behavior is shaped by two primary sources: direct experience with environmental consequences (contingency-shaped behavior) and verbal rules or instructions (rule-governed behavior). Relational Frame Theory (RFT) provides a robust account of how language and cognition allow rules to alter and dominate behavior (Hayes, Barnes-Holmes, & Roche, 2001).

A key finding from this research tradition is the Rule-Based Insensitivity Effect (RBIE): a demonstrated human tendency to adhere to a verbal rule even when it directly contradicts one's immediate experience (Kissi et al., 2020). In a systematic review screening 1,464 records, Kissi and colleagues found that after contingency changes, rule-following groups were more inclined to demonstrate behavior that was reinforced before the change, compared to their non-instructed counterparts. Clinical psychologists have argued the RBIE is at the core of various psychological problems including addiction, depression, and personality disorders (Baruch et al., 2007; Blackledge & Drake, 2013; Hayes & Gifford, 1997).

This is the core mechanism of PA as we model it. An alienating parent provides the child with a set of verbal rules (e.g., "Your father is dangerous," "Your mother doesn't really love you"). The RBIE predicts that a linguistically competent child will begin to follow this rule, becoming progressively insensitive to the positive, direct contingencies of their experience with the target parent (e.g., a fun outing, a loving gesture). Harte and colleagues (2020) demonstrated that this rule-governed pattern emerges consistently around age 5, tracking the development of complex verbal behavior. This provides a developmental basis for why verbal children are particularly susceptible to this form of manipulation.

2.3 Pillar 3: Belief Perseverance and Clinical Thresholds

Once a belief is formed, particularly one central to a person's social world, it is highly resistant to change. Belief perseverance is the tendency to maintain a belief even after the original evidence has been discredited (Anderson, Lepper, & Ross, 1980). This conceptual conservatism operates through confirmation bias (selectively seeking belief-consistent information) and cognitive dissonance reduction (reinterpreting contradictory evidence to preserve the existing belief).

In the context of parental alienation, this maps directly onto the clinical observation that severely alienated children continue to reject the target parent even after the alienating parent stops the alienating behavior, or even after the child is temporarily removed from the alienating parent's influence. In our model, belief perseverance is operationalized as a clinical threshold. Once the child's internal belief state crosses this threshold, the model's rules for updating that belief change. The belief becomes locked-in, meaning the system becomes less sensitive to new experiential data that contradicts the belief and more sensitive to information that confirms it. This is not a binary switch but a phase transition in the system's dynamics.

2.4 Pillar 4: A Concrete Behavioral Taxonomy

To ground the model in clinical reality rather than abstract parameters, we incorporate a taxonomy of specific, observable behaviors identified by researchers as hallmarks of alienation. This taxonomy serves two purposes: (1) it defines the inputs (what the alienating parent does) and (2) it defines the measurable outputs (what behaviors emerge in the child).

Table 1: Parent Alienating Behaviors (Inputs)

Code	Behavior	Description
B1	Denigration	Repeatedly speaking negatively about the target parent in front of the child
B2	Limiting Contact	Interfering with phone calls, visits, or communication between child and target parent
B3	Emotional Manipulation	Asking the child to spy, keep secrets, or carry messages
B4	Loyalty Conflicts	Forcing the child to choose between parents, punishing displays of affection for target parent
B5	Fear Induction	Creating the impression that the target parent is dangerous or unstable
B6	Erasing and Replacing	Removing photos, encouraging child to call stepparent "mom" or "dad," rewriting family narrative
B7	Legal/Administrative Weaponization	Using court proceedings, school registrations, or medical appointments to exclude target parent

Table 2: Child Alienated Behaviors (Outputs)

Code	Behavior	Belief Threshold	Description
C1	Campaign of Denigration	-0.3	Child obsesses about hating the target parent, often parroting the alienating parent's language
C2	Weak Rationalizations	-0.4	Child's reasons for rejection are frivolous, absurd, or clearly borrowed from an adult
C3	Lack of Ambivalence	-0.5	Target parent seen as all-bad, alienating parent as all-good; no nuance
C4	Independent Thinker Phenomenon	-0.5	Child insists their feelings are entirely their own and not influenced by anyone
C5	Reflexive Support	-0.6	Child automatically sides with alienating parent in any conflict, regardless of facts
C6	Absence of Guilt	-0.7	Child feels no remorse for cruelty, dehumanization, or exploitation of target parent
C7	Borrowed Scenarios	-0.7	Child describes events they could not have witnessed, using language beyond their developmental level
C8	Spread to Extended Family	-0.8	Animosity extends to target parent's entire family (grandparents, aunts, cousins)

These behaviors are derived from the clinical literature (Baker, 2007; Gardner, 1985; Bernet et al., 2010) and are presented here with approximate belief-score thresholds at which they are expected to emerge in the simulation.

3. The Computational Model

3.1 Agents

The model consists of three agents:

Child (CH): The central agent. Possesses an internal belief_score about the target parent (ranging from +1.0, fully positive, to -1.0, fully negative), a belief_state (normal or locked-in), and a list of currently exhibited C behaviors.
Target Parent (TP): Modeled with a baseline positive interaction quality. Each interaction generates a positive experience for the child.
Alienating Parent (AP): Modeled with a set of B behaviors they can enact. Each behavior has a probability of being performed at each time step.

3.2 State Variables

Each agent carries state variables that evolve over the course of the simulation:

Child: belief_score (float, -1.0 to +1.0), belief_state (enum: NORMAL, LOCKED_IN), active_c_behaviors (set of C codes), interaction_history (list of weighted experiences)
Target Parent: interaction_quality (float, 0.0 to 1.0, default 0.8), consistency (float, 0.0 to 1.0)
Alienating Parent: b_behavior_probabilities (dict mapping B1-B7 to floats), intensity (float, 0.0 to 1.0)

3.3 Simulation Loop

At each discrete time step t (representing, e.g., one week):

Custody Schedule: Determine which parent the child interacts with based on the custody arrangement for this phase of the experiment.
Interaction Generation:
- If with TP: Generate a positive experience weighted by interaction_quality. The raw positive impact is, for example, +0.05.
- If with AP: Roll against each B behavior probability. For each B behavior enacted, generate a negative impact on the child's belief (e.g., -0.03 per behavior). Also generate any positive bonding experience the AP provides (they are still a parent).
Belief Update (The Core Dynamic):
- Calculate the raw experience delta from Step 2.
- Apply the RBIE Multiplier: The child's current belief_score acts as a filter on positive experiences with the TP. If the belief is already negative, positive experiences are discounted. Specifically: effective_positive_impact = raw_positive * max(0.1, (1 + belief_score) / 2). This means at a belief of -0.8, the child only registers 10% of the positive experience.
- If belief_state is LOCKED_IN, apply an additional Perseverance Dampener: positive experiences toward recovery are further reduced by a factor (e.g., 0.3), while negative confirmatory experiences are amplified by a factor (e.g., 1.5).
- Update belief_score with the effective delta, clamping to [-1.0, +1.0].
C Behavior Emergence: Check the child's belief_score against the thresholds in Table 2. Add or remove C behaviors accordingly.
Threshold Check: If belief_score drops below the CLINICAL_THRESHOLD (default: -0.8) AND the child exhibits 6 or more C behaviors, transition belief_state to LOCKED_IN.
Logging: Record the time step, belief score, belief state, active B behaviors from parent, and active C behaviors from child.

3.4 Key Parameters

Parameter	Default	Description
`CLINICAL_THRESHOLD`	-0.8	Belief score at which lock-in can occur
`MIN_C_FOR_LOCKIN`	6	Minimum C behaviors required for lock-in
`RBIE_FLOOR`	0.1	Minimum fraction of positive experience registered
`PERSEVERANCE_DAMPENER`	0.3	Multiplier on positive recovery when locked-in
`PERSEVERANCE_AMPLIFIER`	1.5	Multiplier on negative confirmation when locked-in
`TIME_STEPS`	520	Number of weeks simulated (10 years)

4. Experimental Design

We propose four core experiments, each building on the last.

4.1 Experiment 1: Control (No Alienation)

Setup: Two neutral parents. AP has all B behavior probabilities set to 0. TP interaction quality is 0.8.
Hypothesis: The child's belief_score will remain stable around its initial value (+0.5). No C behaviors will emerge. This establishes the baseline dynamics of the model.

4.2 Experiment 2: Alienation Trajectory

Setup: TP is neutral/positive (interaction quality 0.8). AP has B1-B5 active at moderate probabilities (0.3-0.6 each).
Hypothesis: The child's belief_score will progressively decline. C behaviors will emerge in the order predicted by their thresholds (C1 first, C8 last). Eventually, the belief will cross the clinical threshold and the state will transition to LOCKED_IN.
Key Metric: Time-to-lock-in. How many time steps does it take for the child to reach the locked-in state? This represents the "window of opportunity" for intervention.

4.3 Experiment 3: Intervention with Continued Exposure

This is the first of the two critical recovery experiments. It simulates a scenario where the alienating parent is identified by a clinician but cannot be removed from the child's life.

Setup: Run Experiment 2 until the belief_state is LOCKED_IN. Then, at time step T_intervention, set all of AP's B behavior probabilities to zero. The AP remains in the simulation as a neutral parent. The TP also remains with full positive interaction quality.
Hypothesis: The child's belief_score and C behaviors will fail to recover to baseline within a clinically meaningful timeframe (e.g., 2 years / 104 time steps). The locked-in belief perseverance dynamics will maintain the negative belief even in the absence of new alienating inputs.

4.4 Experiment 4: The 50/50 Custody Recovery Test

This is the most clinically relevant experiment. It simulates a court-ordered equal time arrangement applied after severe alienation has already taken hold.

Setup: Run Experiment 2 until the belief_state is LOCKED_IN. Then, at T_intervention, switch to a strict 50/50 custody schedule. The TP provides consistently positive interactions. The AP continues to perform B behaviors at their original rates.
Hypothesis: The child's belief_score will fail to recover and may continue to decline. The 50% exposure to positive experiences will be insufficient to overcome the combined effect of (a) continued alienating input during the other 50% of the time and (b) the locked-in belief system discounting positive experiences. This would computationally demonstrate that equal custody, while intuitively fair, is therapeutically insufficient when applied after severe alienation.

4.5 Experiment 5: Early Intervention Comparison

Setup: Run the alienation trajectory, but intervene (set B behaviors to zero) at three different points: (a) when 2 C behaviors are present, (b) when 4 C behaviors are present, and (c) after full lock-in.
Hypothesis: Recovery time and completeness will be dramatically better for earlier interventions. This would provide computational evidence for the critical importance of early identification.

5. Anticipated Results and Plots

The simulation will produce the following visualizations:

Belief Trajectory Plot: A line graph showing belief_score over time for all five experiments on the same axes, with the clinical threshold marked as a horizontal line.
C Behavior Accumulation Plot: A stacked area chart showing the number of active C behaviors over time for each experiment.
B-to-C Mapping Heatmap: For Experiment 2, a heatmap showing which specific B behaviors most strongly predict the emergence of each C behavior.
Recovery Comparison Plot: For Experiments 3, 4, and 5, a comparison of belief trajectories after intervention, showing the dramatically different recovery curves.
Sensitivity Analysis: Plots showing how variations in key parameters (e.g., RBIE_FLOOR, PERSEVERANCE_DAMPENER) affect the time-to-lock-in and recoverability.

6. Discussion

6.1 Implications for Legal Decision-Making

If the model's predictions hold, the results would provide a concrete, visualizable argument against the common judicial assumption that "equal time fixes everything." The simulation would demonstrate that by the time alienation reaches the severe stage, a 50/50 custody order is not a therapeutic intervention but a maintenance condition for the child's suffering. This has direct implications for how courts should structure remedial custody orders.

6.2 Implications for Clinical Practice

The model provides clear markers for clinical assessment. By mapping the child's observable C behaviors onto the model's trajectory, a clinician could estimate where on the alienation curve a particular child falls and, critically, whether they have crossed the clinical threshold. This transforms assessment from a subjective impression into a structured, behavior-anchored evaluation.

6.3 The Window of Intervention

Experiment 5 is designed to quantify the "window of intervention." If the model demonstrates that intervening when only 2 C behaviors are present leads to full recovery within months, while intervening after lock-in leads to negligible recovery even after years, this provides the strongest possible argument for early screening and intervention in high-conflict custody cases.

6.4 Limitations

This model is a simplification. It does not account for:

The child's temperament, intelligence, or pre-existing attachment security
The influence of extended family, peers, therapists, or other social supports
Variability in the child's developmental stage over the 10-year simulation
The target parent's own potential for negative behaviors (the model currently treats TP as consistently positive)
Cultural and socioeconomic factors

These limitations are acknowledged as directions for future model development, not as invalidations of the core framework.

7. Future Directions

Monte Carlo Simulation: Running thousands of iterations with randomized parameters to generate probability distributions rather than single trajectories.
Multi-Child Models: Simulating sibling dynamics, where one child may be more susceptible to alienation than another.
Therapist Agent: Adding a fourth agent representing a family therapist who applies specific, evidence-based interventions at defined points.
Validation Against Clinical Data: Comparing the model's predicted trajectories against longitudinal case data from family court records.

8. Conclusion

This paper lays the theoretical and methodological groundwork for a computational approach to studying parental alienation. By synthesizing agent-based modeling, Relational Frame Theory's Rule-Based Insensitivity Effect, the psychology of belief perseverance, and a clinically-grounded behavioral taxonomy, we create a falsifiable model that captures the essential dynamics of this complex problem. The proposed experiments are designed to answer the questions that matter most to affected families: How does alienation develop? When does it become resistant to change? And what does it actually take to help a child recover?

By translating psychological theory into a computational experiment, we bring new clarity to a field in need of it. The model's potential as an educational tool for judges, mediators, and clinicians may prove as valuable as its research applications.

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Edited by Rob Spain, BCBA, IBA

Correspondence: rob@reunifyscience.com

This paper represents ongoing research at Reunify Science. The computational model described herein is currently being developed and will be made available as open-source software upon completion of initial experiments.