Fair Atomic Governance — Paper 3

Paper 3 of the Agent Governance Series.

Admission control determines what can happen. Fairness determines who gets to act.
Correctness is local. Fairness is global.

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Paper

Fair Atomic Governance: Allocating Decision Boundaries under Shared Resource Constraints in Multi-Agent Systems
Marcelo Fernandez (TraslaIA), 2026

DOI: 10.5281/zenodo.19672597  ·  arXiv: under review

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What this is

This repository contains the LaTeX source for Paper 3 of the Agent Governance Series — a formal theory paper that characterizes the allocation layer above the atomic decision boundary.

The core problem: Atomic decision boundaries (Paper 0) guarantee that every individual admission decision is correct. In a multi-agent system, however, per-agent bounded enforcement creates a global capacity K = N · k₀ that scales linearly with agent count. A single actor controlling m agents can capture m · k₀ admissible actions — its entire pro-rata share — without any individual agent exceeding its local bound. The system is correct at every decision point and yet arbitrarily unfair in aggregate.

The paper introduces:

• The allocation layer: the formal mechanism that determines which agent's pending request is presented to the atomic boundary at each step — independent of the correctness of the boundary itself.
• Three failure modes consistent with full atomic correctness: Sybil amplification, temporal domination, and resource contention unfairness.
• A fairness hierarchy for atomic governance: share fairness, actor-level proportionality, envy-freeness, and strategy-proofness.
• Four allocation mechanisms (M1–M4) with proofs of which fairness properties each achieves.

Paper 0 (DBM): https://github.com/chelof100/decision-boundary-model
Paper 1 (ACP): https://github.com/chelof100/acp-framework-en
Paper 2 (IML): https://github.com/chelof100/iml-benchmark
Paper 4 (Compositional): https://github.com/chelof100/compositional-governance
Paper 5 (RAM): https://github.com/chelof100/reconstructive-authority-model

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Repository contents

fair-atomic-governance/
├── main.tex          # Full LaTeX source
├── references.bib    # Bibliography
├── main.pdf          # Compiled paper (27 pages)
├── README.md
├── LICENSE
└── .gitignore

This is a theory paper with formal experiments. The contribution is entirely formal.

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Formal results

Theorem 5.1 — Sybil Amplification

Under per-agent bounded enforcement with bound k₀ and an identity-oblivious allocation function, the actor share satisfies:

S_{u_j} = m_j / N

where m_j = |A_j| is the number of agents controlled by actor u_j. Registering additional agents increases actor share linearly: ∂S_{u_j}/∂m_j = 1/N > 0. No identity-oblivious mechanism can guarantee ε-actor-level proportionality for ε < max_j |m_j/N − 1/M|.

Theorem 5.3 — Allocation Necessity

There exists a multi-agent system in which F satisfies the atomic decision boundary property (every admitted action is atomically correct) and the trivial FCFS allocation function, such that actor-level proportionality fails with maximum deviation |S_{u_j} − 1/M| = 1/2. Atomic correctness does not imply fair allocation; an explicit allocation layer is a necessary additional component.

Theorem 5.4 — Strategy-Proofness Impossibility

Under per-agent independent enforcement, no allocation mechanism can simultaneously achieve:

• (i) ε-actor-level proportionality, and
• (ii) strategy-proofness against identity fragmentation.

Any actor-aware mechanism that achieves both must aggregate state across agents of the same actor, breaking per-agent independence. This is a governance-layer analogue of the Gibbard–Satterthwaite theorem.

Mechanism comparison

Mechanism	Share Fair	Actor Prop.	Strategy-Proof	Starvation-Free
M1 — Per-Agent Token Bucket (ACP baseline)	≈	✗	✗	✓
M2 — Round-Robin Fair Queuing	✓	✗	✗	✓
M3 — Actor-Aware Rate Limiting	✓	✓	✓	✓
M4 — WFQ (uniform weights)	✓	✗	✗	✓
M4 — WFQ (actor weights 1/m_j)	≈	✓	✓	✓

Interaction with Escalation and IML

• Escalation queue fairness: The Escalate outcome (Paper 0, Corollary 4.5) creates a pending-review queue that is itself a resource subject to contention. Actor-aware queuing (M3 applied to the escalation scheduler) prevents actors from dominating supervisor attention.
• Allocation bias as behavioral drift: Persistent allocation skew induces IML drift. An over-served agent's empirical tool distribution diverges from its admission-time baseline P_{E₀}, increasing D̂(τ, A₀) even though g(τ) = 0 throughout. Allocation fairness and IML monitoring are complementary: M3/M4 prevent false IML positives caused by over-service.

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The governance architecture

┌──────────────────────────────────────────────────────┐
│  L5 — RAM               [Paper 5, RAM]               │  When to execute under partial observability?
├──────────────────────────────────────────────────────┤
│  L3 — Allocation        [Paper 3, this repo]         │  Who gets to act?
│  Fair scheduling across agents                       │
├──────────────────────────────────────────────────────┤
│  L2 — IML               [Paper 2, iml-benchmark]    │  Has behavior drifted?
│  Behavioral drift within g⁻¹(0)                     │
├──────────────────────────────────────────────────────┤
│  L1 — ACP               [Paper 1, acp-framework-en] │  Is this action admissible?
│  Stateful per-action admission control               │
├──────────────────────────────────────────────────────┤
│  L0 — Atomic Boundary   [Paper 0, decision-boundary] │  Can guarantees be made?
│  Decision + transition as a single LTS step          │
└──────────────────────────────────────────────────────┘

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Position in the series

Paper	Title	Repo	Status
Paper 0	Atomic Decision Boundaries	decision-boundary-model	Zenodo · arXiv:2604.17511
Paper 1	Agent Control Protocol (ACP)	acp-framework-en	Zenodo · arXiv:2603.18829
Paper 2	From Admission to Invariants (IML)	iml-benchmark	Zenodo · arXiv:2604.17517
Paper 3	Fair Atomic Governance (this repo)	fair-atomic-governance	Zenodo · arXiv: under review
Paper 4	Irreducible Multi-Scale Governance	compositional-governance	Zenodo · arXiv: under review
Paper 5	Reconstructive Authority Model (RAM)	reconstructive-authority-model	Zenodo · arXiv: under review

Series logic:

• Paper 0 proves when admissibility can be guaranteed (structural necessity of atomic boundaries).
• Paper 1 builds a protocol that satisfies that condition (ACP, with TLA+ verification).
• Paper 2 operates above the boundary to detect behavioral drift invisible to enforcement.
• Paper 3 proves that correct enforcement does not imply fair allocation, and characterizes the allocation layer (this paper).
• Paper 4 composes all layers and proves their joint necessity (irreducibility).
• Paper 5 provides the operational closure: given partial observability, determines when execution is valid at runtime (RAM).

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Citation

@misc{fernandez2026fair,
  title        = {Fair Atomic Governance: Allocating Decision Boundaries under
                 Shared Resource Constraints in Multi-Agent Systems},
  author       = {Fernandez, Marcelo},
  year         = {2026},
  doi          = {10.5281/zenodo.19672597},
  howpublished = {\url{https://doi.org/10.5281/zenodo.19672597}},
  note         = {Paper~3 of the Agent Governance Series. Zenodo. arXiv: under review.}
}

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Author

Marcelo Fernandez — TraslaIA — info@traslaia.com
https://agentcontrolprotocol.xyz