Ensembles Fail When Errors Correlate — hypothesis
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hypothesis.md
# Ensembles Fail When Errors Correlate — hypothesis **Source:** Incoprea Theory Volume VIII, Theory 065 / Information & Computation. **Claim (verbatim):** "Ensemble benefit disappears when member errors correlate above a threshold, so adding a highly accurate but correlated model can reduce the ensemble's reliability despite raising its average accuracy." **Predictions (verbatim):** - P1 — Ensemble gain should vanish above an error-correlation threshold. - P2 — Adding accurate correlated members should reduce reliability. - P3 — Correlation should predict gain better than member accuracy. **Refutation (verbatim):** Gains persisting at high correlation would leave averaging as the explanation. **Pre-registered test.** Build three binary classifiers whose errors share a common source (a latent shock) to set their pairwise error correlation, while keeping each member's individual error rate fixed. Majority-vote the three. Measure how the ensemble's error reduction over a single member behaves as the correlation rises (P1), whether an accurate-but-correlated third member underperforms an equally accurate independent one (P2), and whether correlation or accuracy is the stronger predictor of the gain across a grid of ensembles (P3). **Fixed before running:** majority vote of three members; correlation set by a shared error shock; member error rates held constant within each comparison.