0. Technical Preliminaries

Before any argument about auditing can proceed, it is worth fixing precisely what the Lens Model Equation says — because the easiest mistake to make, and the one most quickly spotted by any reader trained in judgment and decision-making, is to start by describing it incorrectly.

In Tucker's (1964) classic formulation, achievement — the correlation between the judge's judgment and the distal criterion, $r_a$ — decomposes as:

$$r_a = G \cdot R_e \cdot R_s + C\sqrt{1-R_e^2}\sqrt{1-R_s^2}$$

where:

• $R_e$ — environmental predictability: the multiple correlation between the available set of cues and the real distal criterion.
• $R_s$ — judge consistency: the multiple correlation between the cues and the judgment actually produced, across equivalent configurations.
• $G$ — matching: the linear correspondence between the weights the judge assigns to each cue and the ecologically valid weights of those same cues in the real environment. This is the component that carries the central normative claim of any audit built on the LME — that it is possible to detect when a judge, human or algorithmic, is using the wrong cues, or weighing the right ones in a way misaligned with their real validity.
• $C$ — residual correlation: the covariation between the residuals of the two linear models (the environment's and the judge's) that is not captured by the $G \cdot R_e \cdot R_s$ component — generally interpreted as non-linear or configural knowledge, not modeled by the regression.

The distinction between $G$ and $C$ is not a matter of notational preference. $G$ measures whether the judge uses the right cues, with the right weights, linearly; $C$ measures everything else — what remains once that linear correspondence has been removed. Confusing the two — attributing to $C$ the meaning that belongs to $G$, or vice versa — is not a minor slip: it inverts the exact mechanism the audit is meant to expose. An auditing instrument whose description of its own internal mechanics is incorrect does not inspire confidence as a standard for evaluating anyone else, regardless of how rigorous the argument that follows may be.

A second precision matters equally, more conceptual than notational: the LME is an algebraic identity about correlations, not a decomposition of independent error sources that sum causally. Treating $R_e$, $R_s$, $G$, and $C$ as though they were four distinct causes of failure, each isolable and separately fixable, is already a reification of the formal apparatus — the equation describes how the overall correlation relates algebraically to these four terms, not how each term causes a fraction of the observed error. This distinction between algebraic description and causal explanation runs through many of the objections this article confronts later on, and it is easier to keep in view if stated here, before any application of the equation to a concrete case, than recalled midway through an argument already underway.

(Bibliographic note: the most cited systematic review of algorithm aversion in this literature is Burton, Stein & Jensen — the correct citation is 2020, Journal of Behavioral Decision Making, 33(2), 220–239; the article was published online-first in October 2019, which accounts for the year confusion that sometimes appears in other sources.)