papers/zoo-poai-consensus/sections/05-quality-scoring.tex

\section{Quality Scoring}

\label{sec:quality}

\subsection{Multi-Party Evaluation}

Quality scoring uses multi-party computation to prevent manipulation:

\begin{algorithm}[t]
\caption{Multi-Party Quality Evaluation}
\label{alg:mpe}
\begin{algorithmic}[1]
\STATE \textbf{Input}: Attestation $A$, validator set $V$
\STATE \textbf{Output}: Consensus quality $Q$
\STATE Each validator $v$ computes $q_v(A)$ independently
\STATE Validators commit $c_v = \text{Hash}(q_v \| r_v)$
\STATE Wait for all commits
\STATE Validators reveal $(q_v, r_v)$
\STATE Verify $c_v = \text{Hash}(q_v \| r_v)$ for all $v$
\STATE $Q \leftarrow \text{TrimmedMean}(\{q_v\}, 0.1)$
\RETURN $Q$
\end{algorithmic}
\end{algorithm}

\subsection{Evaluation Metrics}

\textbf{Inference Tasks}:
\begin{equation}
q_{\text{inf}} = \frac{\text{correct outputs}}{\text{total outputs}} \cdot (1 - \text{latency penalty})
\end{equation}

\textbf{Training Tasks}:
\begin{equation}
q_{\text{train}} = \Delta_{\text{val}} \cdot e^{-\lambda \cdot \text{cost}}
\end{equation}
where $\Delta_{\text{val}}$ is validation accuracy improvement.

\textbf{Experience Extraction}:
\begin{equation}
q_{\text{exp}} = \text{novelty} \cdot \text{applicability} \cdot \text{correctness}
\end{equation}

\subsection{Gaming Resistance}

The trimmed mean resists Byzantine manipulation:

\begin{theorem}[Byzantine Resistance]
With $f < n/3$ Byzantine validators, the trimmed mean with 10\% trim differs from the honest median by at most $2\sigma / \sqrt{n-2f}$.
\end{theorem}