How Many Humans Are 32 LLM Judges Worth?

Chao Li, Yingying Yu, Yunfeng Li

A panel's human-equivalent size is target-specific. Matching a fixed 32-judge panel to empirical human label distributions on three ChaosNLI tasks yields two distinct effective sizes: distributional-error matching gives $ν_{\mathrm{MSE}}=2.304$, $3.750$, and $3.445$, whereas spectral matching gives $ν_H=4.242$, $6.459$, and $6.499$, a gap of $1.72$--$1.89\times$; a binary-error diagnostic credits the same panels with only $1.971$--$2.227$ effective votes. Extrapolating the distributional-error curve at fixed squared mean residual, mean member variance, and normalized mean covariance gives asymptotes of $2.392$, $3.990$, and $3.655$, with 32 judges already reaching $94.0$--$96.3\%$. An exact spectral identity explains the gap: error depends on member energy and on the orientation of residual variation relative to averaging, information that the participation ratio (PR) discards. A realizable hard-label construction confirms that higher spectral diversity can coexist with worse distribution recovery even under equal member energies and nonnegative correlations, and the consensus direction retains $γ_{\mathrm{co}}=43.8\%$, $33.7\%$, and $35.9\%$ of centered residual variance. An…