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Equation 4 · Part 3 · Agent Evaluation in 2035: Two Axes, Four Scenarios, and What Would Falsify Them

Symbol epsilon_max

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}
ϵmax⁡\epsilon_{\max}

What this part means

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

Its job in the formula

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

The passage around this formula

…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 the second clause is the one Axis A supplies or withholds. Zheng and colleagues’ own…

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