A Decision-Theoretic Extension of Causal Unit Selection: Identifiability, Threshold Rules, and the Fallacy of Naive Benefit Rates.

Abstract and Overview This repository contains the official preprint and python replication code for the research paper "A Decision-Theoretic Extension of Causal Unit Selection: Identifiability, Threshold Rules, and the Fallacy of Naive Benefit Rates" (Eskelinen, Version 3). The work formalizes and advances the principles of individualized causal decision-making by extending the foundational Li-Pearl (2021) benefit function into a rigorous decision-theoretic framework. While standard unit-selection frameworks focus on bounding unobserved counterfactual response types (Benefited, Always-taker, Never-taker, and Harm), this paper derives explicit operational decision rules for group selection under latent confounding, missing counterfactual data, and sample size constraints. Version 2 expanded the empirical validation to financial markets and introduced an applied advisory layer implementation. Version 3 extends these theorems directly into an LLM Agent Autonomy Guardrail, providing a mathematically derived gate to determine exactly when an AI agent should act autonomously versus when it is forced to defer to a human. Core Mathematical and Theoretical Contributions Theorem 5 (Identifiability): We provide a strict mathematical proof demonstrating that the target benefit function f(c) is point-identifiable purely from observable causal effects if and only if the structural master coefficient sigma (defined as beta - gamma - theta + delta) equals exactly zero. When sigma is non-zero, counterfactual shifts alter the true function value while holding observable margins constant. Theorem 6 (Decision Criterion and the Abstain Rule): Under fundamental counterfactual uncertainty where the Probability of Necessity and Sufficiency (PNS) is unknown, we prove that target groups c0 and c1 are strictly decidable if and only if the absolute difference between their risk-adjusted weights, |W1 - W0|, strictly exceeds the absolute value of the master coefficient sigma. If this condition is not met, the mathematical intervals overlap, and the optimal action is to completely abstain from selection. Theorem 7 (Reliability Under Estimation): Assuming a true gap margin D = |W1 - W0| - |sigma| > 0, we prove that the decision rule yields zero active errors, where the required empirical sample size scales proportionally to 1/D². Below this threshold, additional data yields diminishing returns and cannot resolve structural uncertainty. Theorem 8 (Autonomy Criterion - New in v3): Extending T5–T7 to agent environments, we prove an agent's action is strictly and decidably better than deferring to a human if and only if |gamma - delta| * |p_a - p_h| > |sigma| (where p_a is the agent's success rate and p_h is the human's). This decision represents a pure agent-vs-human comparison and is completely independent of the status quo. Theorem 9 (Abstain Safety - New in v3): Under the autonomy decision rule, the agent never acts autonomously when the action would be harmful (active error approaches 0). The explicit weight of harm (delta) expands the structural margin |sigma|, enforcing that critical infrastructure mathematically requires significantly stronger evidence before autonomy is permitted. Empirical Validation and the Naive Fallacy Healthcare Data (TWINS): Validated on the Louizos et al. TWINS dataset (n=71,345), the framework exposes a severe structural flaw in traditional naive benefit rates (a - b = PNS - P(H)). While the naive metric captures 40% of the true benefit in low-risk populations, it collapses to a massive 14-fold underestimation (0.19% vs a true 2.7%) in high-harm strata (such as the preterm segment) because equal probabilities of true benefit and active harm cancel each other out in the aggregate. Financial Market DGP and yfinance Data: The theoretical mechanism was successfully transferred to trading decisions. Validated on synthetic segmentations and roughly 3 years of public market data (380 non-overlapping decision units), the framework demonstrates how observable counterfactuals (e.g., independent benchmark movements) close the uncertainty gap. The structural interval successfully bounds true utility in real-world trading environments. LLM Guardrail Validation (FiFAR / OpenL2D - New in v3): The agent autonomy gate (T8/T9) was validated against a public fraud dataset featuring AI decisions versus 50 synthetic human analysts (n=30,622 cases). The framework correctly executed 54/54 segment decisions, demonstrating precisely when to grant autonomy (ACT) and when to enforce human deferral (ABSTAIN) based on explicit utility rather than heuristic confidence thresholds. The Advisory Layer Implementation Building on the theoretical foundation, this framework introduces a quantitative advisory layer for decision audits. Rather than forcing point estimates, the system explicitly encodes the decision-maker's risk tolerance into the utility parameters and functions as a structural gatekeeper. It reads decision data and automatically defaults to an "abstain" state when the effects fall within the structural margin of error, effectively preventing overconfidence in small sample sizes. File Index and Structural Manifest A_Decision_Theoretic_Extension_of_Causal_Unit_Selection_v3.pdf - Full updated preprint manuscript containing the complete formal theorems, proofs, algebraic derivations, the empirical setups for financial markets, and the new LLM agent autonomy guardrail extensions. unit_selection_theorems.py - Original replication script containing the algorithmic implementation of the bounding theorems and TWINS dataset validation protocols. market_validation_scripts.py - Replication code for the synthetic market DGP and yfinance real-world data validation. v3_guardrail_validate.py - Standalone Python script for validating the LLM autonomy gate. Contains inline mathematics with zero complex import dependencies for base levels. Features Monte Carlo verification (192 combinations), automatic TWINS integration, optional FiFAR dataset validation, and configurable custom utility parameter testing. License: Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0)