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

Abstract

The problem of causal unit selection aims to target interventions by maximizing net benefit across unobserved response types: Benefited, Always-taker, Never-taker, and Harm. This paper extends the Li–Pearl (2021) benefit function $f(c) = W(c) + \sigma \cdot \text{PNS}(c)$ into a purely decision-theoretic framework. We prove that the benefit function is point-identifiable from experimental effects if and only if the system master coefficient $\sigma = 0$. We establish a strict dominance threshold $\vert{}W_1 - W_0\vert{} > \vert{}\sigma\vert{}$ required for safe group selection, below which the mathematically optimal behavior is to abstain. Empirical validation on the TWINS dataset confirms the necessity of this abstain behavior under finite data. Furthermore, we demonstrate that the traditional naive benefit rate ($a - b$) collapses to a 14-fold underestimation of true benefit in high-harm segments, highlighting the critical danger of ignoring strict causal constraints in practical unit selection.