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Equation 5 · Part 8 · Frontier AI Model Comparisons: A First-Principles Introduction

subtraction

P(A≻B)=11+e−(θA−θB).P(A \succ B) = \frac{1}{1 + e^{-(\theta_A - \theta_B)}}.
subtraction

What this part means

Subtract the following term or group from the preceding one. A leading minus marks a negative quantity.

Its job in the formula

Subtract the following term or group from the preceding one. A leading minus marks a negative quantity.

The passage around this formula

A different style of evaluation sidesteps fixed question sets altogether by asking humans which of two anonymized model outputs they prefer, on real conversational prompts, and aggregating millions of these paired judgments into a ranking. Chatbot Arena, the platform behind this approach, describes itself as using “a pairwise comparison approach” that “leverages input from a diverse user base through crowdsourcing,” with the underlying statistics resting on a standard paired-comparison model rather than a raw win count [ 6 ] . The relevant object is a Bradley–Terry model: each system i is assigned a latent strength θi\theta_i , and the estimated probability that system A ’s output is preferred…

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Learn the underlying idea

Addition combines quantities; subtraction measures the signed difference between them. Parentheses show what is combined before the rest of the expression is evaluated.

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Sources cited in the surrounding passage

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