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Equation 7 · Part 3 · The Main Technical Approaches to AI Alignment, Compared

Symbol E_τsim(pi_1,pi_2)

max⁡π1  min⁡π2    Eτ∼(π1,π2)[Judge(τ)],\max_{\pi_1}\;\min_{\pi_2}\;\; \mathbb{E}_{\tau\sim(\pi_1,\pi_2)}\big[\mathrm{Judge}(\tau)\big],
Eτ∼(π1,π2)\mathbb{E}_{\tau\sim(\pi_1,\pi_2)}

What this part means

E_τsim(pi1i_1,pi2i_2) is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Its job in the formula

E_τsim(pi1i_1,pi2i_2) is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

The passage around this formula

Debate targets the oversight ceiling directly rather than working around it, and its motivation is stated in explicitly theoretical terms. Irving, Christiano, and Amodei propose training two agents through self-play in a zero-sum game: each argues a position in alternating statements, and a human judge decides which one gave more true, useful information. The paper’s central theoretical claim draws an analogy to computational complexity theory, arguing that if optimal play in the debate game tracks truth, then a judge with only polynomial-time reasoning ability could in principle adjudicate a debate about problems in the complexity class PSPACE — that is, questions considerably harder than…

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Sources cited in the surrounding passage

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