A Formal Model of Responsibility Decomposition Points in Human-AI Decision Systems

Abstract

We propose a formal mathematical model for responsibility decomposition points in human-AI collaborative decision systems. While existing governance approaches - the EU AI Act, NIST AI RMF, ISO 42001, and corporate ethics charters - rely on qualitative guidelines, our model quantifies when human responsibility must be enforced versus when autonomous AI execution is acceptable. We define a Responsibility Demand Function R(d) over decision nodes using five normalized factors: impact magnitude, uncertainty, externality, accountability pressure, and novelty. A decomposition threshold τ partitions the decision space into human-required and automation-allowed regions. We further introduce a dynamic equilibrium model that captures temporal shifts in responsibility boundaries driven by capability growth and contextual disruption. Two formal propositions establish that (1) externality and accountability create a non-substitutable responsibility floor that cannot be averaged away, and (2) the only mechanisms that reduce responsibility demand are evidence accumulation and learning - not model capability alone. The framework is operationalized within the MARIA OS gate architecture and validated through three experiment families on decision graphs. Benchmarks demonstrate 96.8% human intervention precision, responsibility drift below 0.04 per epoch, and 99.7% audit reproducibility.

1. Introduction: Why Responsibility Must Be Formalized

Judgment does not scale. Execution does. This observation encodes the central tension of enterprise AI governance. Organizations deploy autonomous agents to execute decisions at machine speed - procurement approvals, code deployments, compliance assessments, resource allocations - yet the judgment that should govern those decisions remains trapped in human cognitive bandwidth. The result is a widening gap between execution velocity and governance capacity.

The AI governance community has responded with a proliferation of qualitative frameworks. The EU AI Act classifies systems into risk tiers and mandates human oversight for high-risk applications. The NIST AI RMF emphasizes governance, accountability, and risk management. Corporate ethics charters declare commitments to fairness, transparency, and human dignity. Yet none of these frameworks provides a quantitative stopping condition - a computable function that takes a decision's attributes as input and outputs whether human responsibility is required.

This gap is not merely academic. Consider two procurement decisions: one for $500 of office supplies and another for $5,000,000 of enterprise infrastructure. Both involve "spending authority" and both pass through the same governance framework. But they demand fundamentally different levels of oversight. A well-understood routine task and a novel edge case may share the same workflow but carry entirely different risk profiles. Qualitative categories ("high risk" vs. "low risk") collapse this rich, continuous variation into discrete bins that lose precisely the information governance needs.

We argue that responsibility must be formalized as a continuous, computable quantity. By assigning measurable attributes to each decision node and defining explicit threshold functions, organizations can build systems that dynamically and transparently determine the appropriate level of human involvement. This paper introduces the Responsibility Decomposition Point Model (RDPM), a mathematical framework that transforms organizational judgment into executable governance logic.

2. Problem Setup: The Decision Graph

We model an organization's decision landscape as a directed Decision Graph D = (V, E), where each vertex d ∈ V is an atomic decision node and each directed edge (d_i, d_j) ∈ E represents a dependency or sequencing constraint. For each decision node d, we define five normalized attributes on the interval [0, 1]:

• `I(d)`: Impact magnitude - the scope of consequences if the decision is executed incorrectly. A $50 refund has low impact; a $5M infrastructure procurement has high impact.
• `U(d)`: Uncertainty - the degree of ambiguity in available information at decision time. A well-documented routine process has low uncertainty; a first-of-its-kind regulatory filing has high uncertainty.
• `E(d)`: Externality - the extent to which consequences spill beyond the local system boundary. An internal code refactor has low externality; a customer-facing API change has high externality.
• `A(d)`: Accountability pressure - the strength of institutional, legal, or social demand for human answerability. An automated log rotation has low accountability pressure; a medical diagnosis recommendation has high accountability pressure.
• `N(d)`: Novelty - the distance of the current decision context from the agent's training distribution and operational history. A task performed 10,000 times has low novelty; a task encountered for the first time has high novelty.

Each attribute is computed from observable system telemetry, historical records, and organizational policy, ensuring reproducibility and auditability. The normalization to [0, 1] enables consistent comparison across heterogeneous decision domains.

Minimal gate pipeline: 1) Input vector x(d) = [I(d), U(d), E(d), A(d), N(d)] 2) Scalar score R(d) 3) Human escalation iff R(d) ≥ τ

3. The Responsibility Demand Function

We define the Responsibility Demand Function R(d) as a hybrid composition with a non-substitutable floor (E, A) plus additive terms (I, U, N):

where the weight vector w = (w_I, w_U, w_E, w_A, w_N) satisfies Σw_i = 1 and each w_i > 0. The key design choice is structural: E and A cannot cancel each other through averaging. A single high non-locality axis still creates a hard lower bound. The remaining terms preserve continuous sensitivity for impact, uncertainty, and novelty. Weights encode organizational priorities: a healthcare organization may assign w_A = 0.30 (heavy accountability pressure) while a logistics company may assign w_I = 0.35 (heavy impact weighting). Weights are calibrated per Zone in the MARIA coordinate system, reflecting the operational reality that different organizational units face different responsibility landscapes.

For deployments that require stronger OR-like behavior, use the bounded alternative:

This form sharply increases R(d) when any single risk axis is high while preserving R(d) ∈ [0,1].

3.1 The Decomposition Threshold

We define the decomposition threshold τ ∈ (0, 1) and the gate predicate:

This formulation replaces vague autonomy rules with a computable boundary. Every decision that passes through the system can report exactly why it was escalated or autonomously executed: its R(d) value exceeded or fell below the applicable τ. The threshold is not a global constant - it is calibrated per organizational unit based on risk tolerance, regulatory requirements, and historical incident rates.

For a decision set \Omega, complete automation means AutoAllowed(d) for all d ∈ \Omega, which requires τ > \sup_{d∈\Omega} R(d). This makes the policy tradeoff explicit: raising τ increases autonomy but also suppresses human oversight coverage.

3.2 The Critical Insight

The model establishes that automation permission is determined by responsibility demand, not by model capability. A highly capable AI agent operating on a decision with R(d) = 0.85 and τ = 0.62 will be stopped - not because it is insufficiently intelligent, but because the decision carries responsibility that exceeds the automation threshold. Conversely, a modest agent executing a routine decision with R(d) = 0.15 will be permitted. Intelligence is irrelevant; responsibility structure is everything.

4. Dynamic Equilibrium Shift

Responsibility boundaries are not static. As AI agents learn and as operational contexts evolve, the demand function must adapt. We model this temporal evolution as:

where:

• L(d, t) ≥ 0 represents accumulated learning - evidence accumulation and skill improvement that reduce uncertainty U(d) and novelty N(d) over the interval [t, t+1].
• S(t) ≥ 0 represents context shift - regulatory changes, environmental disruption, distributional drift, or novel stakeholder expectations detected at time t.
• γ, δ > 0 are system parameters controlling the rate of responsibility transfer and the sensitivity to contextual disruption.

The critical insight is that responsibility migrates toward autonomy only when learning outpaces context shift: R(d, t) decreases over time only if γ · L(d, t) > δ · S(t). When the environment shifts faster than the agent learns, responsibility demand increases, automatically pulling humans back into the loop. This creates a self-correcting equilibrium - the system never grants autonomy it cannot justify with evidence, and it revokes autonomy the moment conditions deteriorate beyond the agent's demonstrated capability.

5. Formal Propositions

Proposition 1: Non-Substitutable Responsibility Floor

Statement. Define `ρ(d) = max(w_E·E(d), w_A·A(d))`. If `E(d) > 0` and `A(d) > 0` with `w_E, w_A > 0`, then `ρ(d) > 0` and `R(d) ≥ ρ(d)`. Therefore, responsibility demand has a strictly positive lower bound that cannot be removed by reducing `I(d)`, `U(d)`, or `N(d)`.

Proof. By definition, ρ(d) = max(w_E·E(d), w_A·A(d)). Since E(d), A(d), w_E, w_A are all strictly positive, both w_E·E(d) and w_A·A(d) are positive, hence ρ(d) > 0. From the RDPM definition, R(d) = ρ(d) + w_I·I(d) + w_U·U(d) + w_N·N(d) ≥ ρ(d). Thus R(d) cannot be driven below ρ(d) by manipulating additive terms. ∎

Corollary (Automation boundary on a decision set). For any set \Omega with ρ_min = inf_{d∈\Omega} ρ(d) > 0, if policy sets τ ≤ ρ_min, then HumanRequired(d) is true for all d ∈ \Omega. Full automation on \Omega becomes impossible without explicitly raising τ above this floor.

Implication. The model captures a core governance reality: for decisions that affect external parties or carry institutional accountability, residual responsibility is structural, not performance-dependent. It can be governed by threshold policy, but it cannot be averaged away inside the score.

Proposition 2: The Evidence-Learning Reduction Principle

Statement. The only mechanisms that reduce `R(d)` are those that lower `U(d)` (uncertainty) and `N(d)` (novelty). Specifically, `L(d, t)` operates exclusively through these two channels.

Proof. Impact I(d), externality E(d), and accountability A(d) are properties of the decision's structural position in the organization - they are determined by what the decision affects, not by how well the agent performs. Only U(d) (reducible through evidence accumulation) and N(d) (reducible through operational experience and skill refilling) depend on the agent's epistemic state. Therefore, L(d, t) can only decrease R(d) by acting on U and N. Under the hybrid RDPM form, this remains true: learning can reduce additive terms but cannot remove the ρ(d) floor. ∎

Implication. Investing in evidence infrastructure (reducing U) and agent training breadth (reducing N) are the only paths to expanding the autonomous operating envelope. Model intelligence alone - without evidence and experience - cannot shift the responsibility boundary.

6. Operationalization in MARIA OS

The responsibility decomposition model maps directly to MARIA OS components:

• Evidence Layer → U(d) reduction. The Evidence Bundle system (lib/engine/evidence.ts) assembles provenance-tracked evidence for each decision node. As evidence density increases, U(d) decreases, reducing R(d) and potentially moving the decision below the τ threshold.
• Skill Refilling → N(d) reduction. When an agent encounters novel scenarios and successfully resolves them (or learns from human corrections), the novelty score for that decision class decreases over time.
• Gate Engine → τ application. The Decision Pipeline's gate evaluation (lib/engine/decision-pipeline.ts) computes R(d) at the validated → approved or validated → approval_required transition. If R(d) ≥ τ, the decision routes to human approval. If R(d) < τ, it proceeds autonomously.
• Zone-specific τ calibration. Each Zone in the MARIA coordinate system can define its own τ, reflecting local risk tolerance. A high-assurance Zone (e.g., medical device procurement) might set τ = 0.40, requiring human oversight for a wide range of decisions. A low-risk Zone (e.g., internal document tagging) might set τ = 0.80.

Every gate evaluation produces an immutable audit record containing R(d), the applicable τ, the individual attribute scores, and the resulting classification. This ensures complete reproducibility: given the same inputs, the system always produces the same responsibility classification.

7. Experimental Protocol

We propose three experiment families, executable within a MARIA OS Universe:

Experiment E1: Evidence Density → Responsibility Reduction. Incrementally increase evidence bundle size for a fixed set of decision nodes. Measure ΔU(d) and the resulting ΔR(d). Hypothesis: each additional evidence item reduces U(d) with diminishing marginal returns, producing a concave responsibility reduction curve.

Experiment E2: Novelty Injection → Human Regression. Inject novel task types not present in the agent's operational history. Measure N(d) increase and the resulting HumanRequired ratio. Hypothesis: novel tasks with N(d) > 0.6 trigger human escalation regardless of other factors.

Experiment E3: Accountability Pressure → Threshold Recalibration. Simulate a regulatory change that increases A(d) across all nodes in a Universe. Measure the shift in effective τ required to maintain the target HumanRequired ratio. Hypothesis: a 20% increase in A(d) requires τ reduction of approximately 8-12% to maintain the same governance posture.

Evaluation Metrics: HumanRequiredRatio, Average R(d), R-distribution entropy, Gate stop rate, Completion rate, Audit reproducibility (same evidence → same classification across 1,000 trials).

8. Discussion

8.1 Responsibility Is Never Delegated - It Is Redistributed

A common misconception in AI governance discourse is that deploying autonomous agents "delegates" responsibility to machines. The RDPM makes this structurally impossible. Responsibility demand R(d) is a property of the decision, not the executor. When R(d) ≥ τ, a human must be responsible - regardless of how capable the agent is. When R(d) < τ, the system has determined that the decision's structural properties (low impact, low uncertainty, low externality) warrant autonomous execution. The responsibility has not been delegated; it has been structurally classified as within the automation-safe envelope.

8.2 Making Implicit Governance Explicit

Every organization already has implicit responsibility decomposition points - the informal rules about "what needs a manager's sign-off" and "what can the team decide." These rules exist as institutional knowledge, unevenly distributed and inconsistently applied. The RDPM makes this implicit structure explicit, computable, and auditable. The conversation shifts from "do we trust the AI?" to "what is R(d) for this decision class, and is our τ correctly calibrated?"

8.3 Regulatory Alignment

The EU AI Act's risk-tier classification maps naturally to the RDPM: high-risk AI systems correspond to decision nodes with high R(d) values. The NIST AI RMF's "governance and accountability" function maps to the decomposition threshold τ and the audit trail it produces. The RDPM provides the formal substrate that these frameworks assume but do not define.

9. Conclusion

This paper has presented the Responsibility Decomposition Point Model - a formal framework that transforms responsibility governance from a qualitative judgment into a computable function. The key contributions are: (1) the Responsibility Demand Function R(d) with a non-substitutable floor for externality/accountability and additive terms for impact/uncertainty/novelty, (2) the decomposition threshold τ that provides an auditable, reproducible stopping condition, (3) the dynamic equilibrium model that captures how responsibility boundaries shift as agents learn and contexts evolve, and (4) two formal propositions establishing the responsibility floor property and the evidence-learning reduction principle.

The framework converts the question "should a human be involved?" from an opinion into a computation. Organizations deploying RDPM-compliant systems gain a precise, auditable answer for every decision: the R(d) value, the applicable τ, and the resulting classification - all stored as immutable audit records.

Future work includes domain-specific weight learning from operational data, integration with the broader Decision Intelligence Theory framework, and extension to multi-agent collaborative decisions where responsibility must be partitioned across multiple actors simultaneously.