BDPD³ — Governing the Signal, Not the Symptom: Leading-Indicator Regulation Prevents the Seneca Cascade in a Polycentric Commons

Abstract

A polycentric commons in which one jurisdiction’s industrial pollution flows downwind into its neighbours raises a governance question that is usually framed as which lever — a cap on the process, a levy on the capital stock, a fine on households. Using the BDPD agent-based platform on a Bardi/Seneca three-variable engine (resource R, capital C, pollution P), we show the binding axis is not the lever but the trigger signal. The reason is temporal. Pollution P is a lagging tail of the industrial boom: its growth rate is multiplicative in the capital stock C, so C must already be large before P can rise. A regulator reacting to P is therefore structurally too late — the industrial capacity that will emit the remaining pollutant is already built — and the downwind victim is not saved. Arming the same cap on the capital stock — a leading, player-visible indicator — prevents the cascade and rescues the emitter from its own Seneca cliff. This is a Pareto-improving outcome, not a victim–polluter trade-off. The timing ladder is monotone: the earlier the visible boom is throttled, the more both parties are saved. A structural OFAT robustness sweep confirms that the claims hold across \(k_1\), baseFraction, and linkRate; the full win-win holds up to the integration step \(dt \leq 3.0\).

This paper is the fourth in the BDPD series. BDPD\(^0\) (Brunelli 2026a) establishes the collapse baseline on a logistic substrate; the companion papers add communication and sanctioning (BDPD\(^1\), (Brunelli 2026b)) and nested governance with agent-architecture inversion (BDPD\(^2\), (Brunelli 2026c)). This paper moves from heuristic and LLM agents on logistic dynamics to deterministic agents on a Seneca ODE substrate, where the governance question shifts from who decides to what signal they act on¹.

Keywords: polycentric governance, leading indicator, Seneca cliff, rate-induced tipping, agent-based modelling, common-pool resource.

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1. Transparency and authorship statement. This project was conceived, directed, and validated by the author. A pool of frontier large language models (including DeepSeek (DeepSeek-AI 2026), Anthropic’s Claude (Anthropic 2026), Qwen (Qwen Team 2026), and Z.ai GLM-5.1 (GLM-5-Team et al. 2026)) was employed as a de facto research team — not as conventional writing tools, but as active artificial collaborators — to refine the original idea, explore the design space, implement and iterate on the codebase, draft and revise the manuscript, and stress-test the arguments. Model outputs were source-grounded by prompt, validated by extensive triaging with different models and finally integrated under author supervision.