Who Should Protect a Declining Commons?

1Introduction

When a shared resource declines, someone must convert the scarcity signal into an actual reduction in extraction. The classic institutional question — running from Hardin's tragedy of the commons to Ostrom's field studies of self-governing commons (Governing the Commons, 1990) — is who should hold that corrective loop: a central authority that pools information from many observers, or the local users who act directly on what they see.

The two loci embody a genuine trade-off. Central control pools multiple observations and averages away idiosyncratic noise, but may act on delayed information. Local control observes and acts directly on fresher information, but each individual estimate is noisier. This precision–latency tension suggests a falsifiable prediction:

This paper reports what happened when that hypothesis was tested in a minimal feedback model, and what a subsequent structural audit of the comparison itself revealed. The arc is: a null result on the σ crossover (Section 3); the discovery that the original comparison confounded governance architecture with effective intervention strength (Section 4); a normalization that separates total corrective capacity G from its allocation α (Section 5); and a final result in which ecological structure, not the central–local locus, dominates performance (Section 6). Throughout, the claims are exploratory results within one computational model family, not empirically calibrated causal estimates.

2The legacy 2×2 model

A shared fish stock B_t follows logistic regeneration with a collapse basin below a biological limit B_LIM and rare exogenous shocks ξ_t:

N = 15 agents observe the stock through correlated noisy reports,

so the variance of the pooled mean report is σ²(ρ + (1−ρ)/N): the √N central advantage holds only at ρ = 0, and as ρ → 1 a floor σ²ρ remains that erodes pooling. ρ is an exogenous knob, not endogenous to collapse. The central loop acts on the arithmetic mean of all reports, with a decision lag; its precision advantage thus emerges rather than being hard-coded. The field loop acts on each agent's own reading. Extraction is applied through a proportional/escapement harvest multiplier, followed by health/welfare updates and regeneration.

Four regimes form a 2×2 design of who adapts:

Each active legacy loop receives its full single-loop gain — a design choice whose consequences Section 4 examines. Regimes were originally scored on the composite P = mean sustainability × mean welfare (set to 0 after welfare collapse); the later analysis decomposes this into collapse probability and discounted welfare as separate primary outcomes, keeping P only as a secondary legacy composite. Determinism is frozen with named seed streams (mulberry32) and guarded by a byte-exact regression test (outputs/data/baseline_v0/, tests/regress_v0.sh).

3Results I: observation noise did not produce a central-to-local crossover

No σ-driven central→field crossover in the hypothesized direction was detected. Direct paired inference sharpens this: using identical innovations (paired common random numbers) and a paired bootstrap confidence interval on the difference Δ = P_DF − P_FD, the predicted sequence — positive at low σ, negative at high σ — is not present anywhere in the tested range.

A variance audit explains why the crossover lacked a mechanism to stand on: the √N averaging benefit is not exclusive to the centre. Independent field actions are aggregated by the shared resource itself, and the self-test shows this aggregation receives the same linear 1/N variance reduction. No pooling asymmetry underwrites a crossover.

4Structural audit: the authority–architecture confound

The original DD ("both adapt") conclusions proved strongly dependent on controller composition and unequal effective intervention, not on co-adaptation per se.

Authority ≠ architecture. Legacy DD applied both loops at full gain — multiplicatively. If the central brake alone leaves 70% of extraction and the local brake alone leaves 70%, both together leave 49%: a much stronger total cut. The apparent effect of having two adaptive loops cannot be separated from simply intervening harder. Separating total authority G from its allocation α (K_c = αG, K_f = (1−α)G) and holding G fixed weakened the original "DD most fragile" / "DD sole survivor" patterns.

Composition matters. Even gain-matched multiplicative composition is not allocation-invariant. Only an action-matched additive rule — combining the signals before one shared harvest transform — holds realized intervention fixed as α varies (verified to floating-point precision, max|Δ| < 10⁻¹², and numerically stabilized in audit Stage 5.6).

5The action-matched normalized model

5.1Control capacity G

A correct scarcity signal is wasted without enough capacity to act on it. The control gain G converts a required correction s into an actual cut in extraction:

5.2Allocation α

To break the confound, total control capacity G is held fixed and applied exactly once, to a mixture of the central and local signals:

α = 0 uses purely local-field information; α = 1 purely pooled-central information; 0 < α < 1 a hybrid. It is one control budget, differently allocated. When central and local signals are identical, the interpolation is exactly α-invariant — tested numerically and end-to-end (max|Δ| < 10⁻¹²).

5.3Resource continuum λ

Before asking who should control, one must ask whether the resource already self-throttles. Extraction pressure interpolates between stock-dependent and stock-independent along a continuum:

At λ = 0 extraction falls with the stock (a self-throttling, Schaefer-like reparameterization); at λ = 1 extraction pressure is stock-independent, the tragedy-prone case. λ is a synthetic stock-decoupling parameter — not a fitted ecological threshold, and not an empirical measure of "tragedy intensity." The mechanism pilot also checks a power-form alternative.

5.4Primary outcomes

• collapseRate — welfare-collapse frequency;
• stockCollapseRate — biological-limit crossing frequency;
• discWelfare — discounted harvest/welfare accumulated over the run;
• collapseMargin, minStock — distance to and minimum relative stock.

Discounted welfare includes benefits accumulated before collapse: a cell can have collapseRate = 1 and still report positive welfare. This is not a contradiction — it separates pre-collapse benefit from safety — but it must never be read as safe performance. Read collapseRate first, then welfare conditional on that safety context.

6Results II: ecological structure and viable capacity dominate; allocation is second-order

The final confirmation grid (confirm_grid.csv, 100 trials per cell) fixes G = 1.5, preselected as the Stage-6 pilot's viable/mid level — not tuned on these results — and sweeps λ × α under clean (σ = 0, no lag) and stressed (noise + lag) conditions.

Ecological stock-dependence λ and G-viability dominate. Discounted welfare falls sharply with λ (≈84 → 35 → 16 from stock-proportional to stock-independent at G = 1.5), and collapse becomes near-certain once G is insufficient for the tragedy endpoint.

Authority allocation α is generally second-order. Under clean conditions (σ = 0, Δlag = 0), welfare is exactly α-invariant. Under combined high noise and lag a modest field-leaning tilt appears — e.g. at λ = 0.5: α = 0 gives welfare 46 with collapse rate 0.90, versus α = 1 giving welfare 20 with collapse rate 1.00 — but λ still dominates. The mechanism pilot found interior-α advantages to be rare: they occur only with noise and lag together, are not a clipping artifact, and are not explained by information fusion, since the welfare-optimal α diverges from the MSE-optimal α under noise.

6.1Robustness across G

A descriptive balanced decomposition of the 27 cell means per condition quantifies "larger" on this grid:

These η² values summarize this deterministic grid; they are descriptive effect ranges on the observed factorial grid, not population-level inferential ANOVA estimates or a causal decomposition. They support the ordering only for the reported model, parameter grid, and outcomes.

7Discussion

7.1An ordering of questions, not a universal winner

Within this model family, the result is best read as a hierarchy of diagnostic questions for a declining commons:

1. Does the resource self-throttle? (λ) — the upstream, dominant factor;
2. Is sufficient corrective capacity available? (G) — a prerequisite, not a detail;
3. Is information noisy or delayed? (σ, lag) — the condition under which locus begins to matter;
4. Where should control be allocated? (α) — a conditional, second-order question.

Three implications extend beyond the model, stated as conjectures. First, institutional performance cannot be separated from the resource being governed. Second, monitoring and implementation capacity are prerequisites of governance, not secondary details. Third — the narrow Ostrom-related conjecture — ecological fit and implementation capacity may condition when the central/local locus matters at all.

7.2Scope of the connection to Ostrom

The model directly studies only a narrow subset of institutional design: monitoring quality, information aggregation, decision delay, implementation capacity, and the locus of corrective action.

Accordingly, the simulation does not test Ostrom's design principles as a whole. It motivates the narrower conjecture above; claims about a general precedence ordering among Ostrom's principles would require a richer model or empirical evidence.

8Limitations and future work

• This is a bounded exploratory computational study of one model family: no empirical calibration, no causal identification. λ is a stock-decoupling parameter, not a validated measure of empirical tragedy intensity.
• The limited hybrid advantage under combined noise and delay requires confirmatory analysis: a controlled decomposition of action dispersion vs. correlated-action risk vs. nonlinear/collapse response, in a safety-first confirmatory design.
• Reserved (not run): a Stage-7 safety grid reporting G_min(α, z) and α*(G, z) conditioned on G (no single α*), with sequential one-sided confidence bounds on collapse probability and no assumed monotonicity in G; a steelman Bayesian/estimator ladder applied symmetrically to both loops; and empirical anchoring of σ, ρ, and lag.
• Numerical caveat: ≈5.7% of pilot trials sit within a scale-relative tolerance of the collapse boundary; such classifications are boundary-sensitive, not substantive.
• The model represents monitoring, delay, implementation capacity, and locus of control; it does not test sanctions, conflict resolution, boundaries, nesting, or rule-making rights (Section 7.2).

9Conclusion

Four contributions:

1. No σ-driven central→field crossover was detected in the tested range and power.
2. The original dual-adaptation conclusions depended strongly on controller composition and unequal effective intervention — architecture and authority were confounded.
3. Under action-matched composition, ecological stock-dependence λ and whether total authority G is viable dominate performance.
4. Authority allocation α is generally second-order, with only limited interior-allocation advantages under combined noise and lag.

In this model family, "who governs" became relevant only after ecology and control capacity — a conditional, second-order question. Whether that ordering survives richer institutional structure and empirical calibration is precisely the confirmatory work this exploratory study motivates.

10Reproducibility and artifacts

All results are deterministic and regression-guarded. The executable source of truth is src/phase_diagram_runner.mjs (Node.js 26.0.0); plotting uses Python 3.11 with NumPy and Matplotlib.

git clone https://github.com/memorist17/commons-governance-model
make verify       # verify committed model, data, PDF, and chart hashes
make test         # self-tests + byte-exact legacy regression
make reproduce    # timestamped full run under outputs/runs/ (100 trials/cell)

Variance control uses paired common random numbers with named seed streams; the allocation-invariance self-test verifies max|Δ| < 10⁻¹²; the frozen legacy CSVs under outputs/data/baseline_v0/ must match byte-for-byte. The staged audit trail is in docs/ (AUDIT_STAGE0-4_REPORT.md, AUDIT_STAGE5_REPORT.md, AUDIT_STAGE6_REPORT.md, AGGREGATION_AUDIT.md).

This article is an HTML compilation of the repository's docs/FINAL_REPORT.md, model documentation, and presentation. All figures are embedded from outputs/figures/ (empirical) and presentation/images/ (conceptual). The model, data, figures, and analyses are the author's; the English prose of this article was drafted with AI assistance (Claude) from those materials and reviewed by the author. The claims are exploratory results within one computational model family, not empirically calibrated causal estimates.