Fair Atomic Governance: Allocating Decision Boundaries under Shared Resource Constraints in Multi-Agent Systems

Atomic decision boundaries guarantee that each agent action is evaluated and committed in a single indivisible step, eliminating the time-of-check/time-of-use gap that undermines split evaluation systems. This correctness guarantee, however, operates locally: it determines whether a given state transition is admissible, but not which agent among many competing requestors reaches the boundary to attempt that transition. When multiple agents share governance infrastructure, per-agent bounded enforcement induces a global capacity that scales linearly with agent count. This creates a structural vulnerability — Sybil amplification — in which an actor controlling m agents captures m times the admissible actions without violating any local constraint. We extend the labeled transition system (LTS) model of atomic governance to the multi-agent setting, separating the correctness of individual admission decisions from the fairness of how those decisions are distributed across agents and actors. We formalize three classes of allocation-level failure — Sybil amplification, temporal domination, and resource contention unfairness — and introduce a hierarchy of fairness notions suited to atomic governance: share fairness, actor-level proportionality, envy-freeness, and strategy-proofness. Key results: - Theorem (Sybil Amplification): under per-agent bounded enforcement without actor-level constraints, actor-level fairness cannot be guaranteed regardless of how admission decisions are made. - Theorem (Necessity): admission control alone — even when atomically correct — is insufficient to guarantee fair allocation; fairness requires an explicit allocation layer above the decision boundary. - Theorem (Strategy-Proofness Impossibility): strategy-proofness and actor-level proportionality are jointly unachievable under pure per-agent enforcement, formalizing the cost of identity fragmentation. - Analysis of four allocation mechanisms: per-agent token bucket, round-robin fair queuing, actor-aware rate limiting, and weighted fair queuing — establishing which fairness properties each satisfies and where each fails. This paper is Paper 3 of a 6-paper Agent Governance Series: P0 — Atomic Decision Boundaries (structural foundation). P1 — Stateful enforcement via ACP. P2 — Behavioral drift detection via the Invariant Measurement Layer (IML). P4 — Composition irreducibility: the four-layer architecture is structurally necessary. P5 — Runtime execution validity under partial observability (RAM). Full series (Agent Governance Series, Papers 0–5): P0 — Atomic Decision Boundaries: https://doi.org/10.5281/zenodo.19642166 P1 — Agent Control Protocol (ACP): https://arxiv.org/abs/2603.18829 | https://doi.org/10.5281/zenodo.19642405 P2 — From Admission to Invariants (IML): https://doi.org/10.5281/zenodo.19643761 P3 — Fair Atomic Governance (this paper): https://doi.org/10.5281/zenodo.19643928 P4 — Irreducible Multi-Scale Governance: https://doi.org/10.5281/zenodo.19643950 P5 — Reconstructive Authority Model (RAM): https://doi.org/10.5281/zenodo.19669430