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Equation 4 · Part 1 · Agent Evaluation in 2035: Two Axes, Four Scenarios, and What Would Falsify Them

Symbol a

Judge(a)={automated,ϵ^(a)≤ϵmax⁡(a) and ϵ^(a) externally auditedhuman required,otherwise\text{Judge}(a) = \begin{cases} \text{automated}, & \hat\epsilon(a) \le \epsilon_{\max}(a) \ \text{and}\ \hat\epsilon(a)\ \text{externally audited} \\ \text{human required}, & \text{otherwise} \end{cases}
aa

What this part means

a is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.

Its job in the formula

a is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.

The passage around this formula

Whether automated LLM-judge evaluation becomes trusted for high-stakes decisions is not a third axis; it is mostly a readout of Axis A applied to one specific evaluator. A useful way to see the dependency is to write the automation decision as a threshold rule. Let ϵ^(a)\hat\epsilon(a) be the estimated error rate of a judge on a decision class a , and let ϵmax⁡(a)\epsilon_{\max}(a) be the maximum…

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