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Equation 6 · Part 1 · From Origins to Frontier: A History of Frontier AI Model Comparisons

Symbol P

P(A≻B)=11+10−(RA−RB)/400.P(A \succ B) = \frac{1}{1 + 10^{-(R_A - R_B)/400}}.
PP

What this part means

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

Its job in the formula

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

The passage around this formula

The response, arriving in 2023, was to stop checking against a fixed answer and start recording a preference between two outputs instead. Chatbot Arena built an open platform in which users submit a prompt, receive responses from two anonymized models side by side, and vote for the one they prefer, without knowing which model produced which response; its authors reported collecting more than 240,000 such votes from a broad user base and validated that crowdsourced preferences agreed well with those of a separate panel of expert raters [ 12 ] . Pairwise votes of this kind are naturally converted into a single continuous rating using a Bradley–Terry-style model — the same functional form used…

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Learn the underlying idea

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

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Sources cited in the surrounding passage

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