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Equation 5 · What Alignment Actually Costs

What does this equation mean?

Chuman=n⋅cˉC_{\mathrm{human}} = n \cdot \bar{c}

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Inputs and operationsn × barc
Result or conditionC_human
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This equation states an equality: the expressions on both sides have the same value under the article’s assumptions. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

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ChumanC_{\mathrm{human}}

Symbol C_human

ChC_human is part of the quantity the equation computes from the expression on the right.

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nn

Symbol n

the practical reason the labeller headcounts above are so low.

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cˉ\bar{c}

Symbol barc

barc is one factor in the product that computes the quantity on the left.

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=

=

The expressions on both sides represent the same quantity under the stated assumptions.

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multiplication

multiplication

Multiply the quantities on either side.

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subscript

subscript

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

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How to interpret it

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What the article says around this equation

The unit economics matter because a dataset’s cost is close to linear in its size: Chuman=n⋅cˉC_{\mathrm{human}} = n \cdot \bar{c}. with n comparisons collected at a mean cost cˉ\bar{c} per comparison. The direct comparison published in the RLAIF paper puts numbers on both sides of a genuinely useful substitution. Lee and colleagues estimate that an AI-generated preference label produced with two inference passes of GPT-4 — used to correct for position bias, at an average of about 830 prompt tokens and 61 tokens of chain-of-thought rationale — costs about 0.06 US dollars per example, against about 0.67 US dollars per example for a human label purchased through a commercial annotation service pricing at roughly 0.11 US…
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The unit economics matter because a dataset’s cost is close to linear in its size: Chuman=n⋅cˉC_{\mathrm{human}} = n \cdot \bar{c}. with n comparisons collected at a mean cost cˉ\bar{c} per comparison. The direct comparison published in the RLAIF paper puts numbers on both sides of a genuinely useful substitution. Lee and colleagues estimate that an AI-generated preference label produced with two inference passes of GPT-4 — used to correct for position bias, at an average of about 830 prompt tokens and 61 tokens of chain-of-thought rationale — costs about 0.06 US dollars per example, against about 0.67 US dollars per example for a human label purchased through a commercial annotation service pricing at roughly 0.11 US dollars per fifty words, applied to documents averaging 304 words [ 3 ] . That is better than a tenfold difference in cˉ\bar{c} , and it is the strongest documented economic argument for the shift toward AI feedback that labs including Anthropic and Google have made in various forms. It is not, on its own, evidence that AI feedback is a free substitute: RLAIF’s own comparison measures win rate and cost together and finds the two feedback sources broadly comparable on the tasks tested, not that the human signal was redundant. What the price gap buys is a change in n that a fixed budget can afford, not a change in what a labelled comparison actually measures.

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