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Equation 4 · Part 2 · Agent Evaluation in 2035: Two Axes, Four Scenarios, and What Would Falsify Them

Symbol hatepsilon

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}
ϵ^\hat\epsilon

What this part means

hatepsilon appears in the objective or constraint used by the optimization on the right.

Its job in the formula

hatepsilon appears in the objective or constraint used by the optimization on the right.

The passage around this formula

…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 error a policy is willing to tolerate for that stakes class. A defensible automation rule is 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}. The rule only licenses automation where both clauses hold, and…

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A function assigns an output to each allowed input. The expression f(x) means “apply f to x”.

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