Cross-family rival decomposition and separation of sampling correlation

Extend the leak-free per-case-preference rival decomposition across additional model families and separate within-case sampling correlation from the preference-unexplained residual in wrong-consensus agreement.

Background

The main analysis is conducted on the GPT-4.1 family, while the supplementary Qwen3.5-9B analysis is too small and lacks the rival null required for a comparable decomposition. The paper also notes that positive within-case sampling correlation is not incorporated into the independent-vote reference and cannot be separated from the residual with the current design. The conclusion therefore identifies both a concrete extension across model families and a methodological problem concerning the disentanglement of sampling correlation from the residual channel.

References

These conclusions are bounded by the i.i.d.\ assumption; future work should extend the rival null across model families (the current Qwen arm is too small, lacks a rival null, and uses different $K$), separate within-case sampling correlation from $\delta$, and turn the channel decomposition into explicit uncertainty estimates.

— Decomposing Wrong-Consensus Agreement in LLM Self-Consistency: A GPT-4.1 Case Study  (2608.18795 - Zhang et al., 19 Aug 2026) in Section 6, Conclusion