Multi‑path reasoning methods such as Self‑Consistency (SC) sample $K$ reasoning paths and pick the answer that appears most often. Empirically, performance quickly plateaus as $K$ grows, and existing techniques do not tell when saturation will happen. We formalize multi‑path LLM reasoning as a diversity combining problem from wireless communications: each path is a noisy channel observation, and the pairwise correlation of path correctness caps the effective sample size of the vote at a finite ceiling.\ Under exchangeability, Generalized Least Squares (GLS) analysis shows that the optimal symmetric linear combiner of latent embeddings assigns uniform weights, which justifies majority vote as the natural default in standard SC while leaving room for weighting or pruning when prompt‑template branches are heterogeneous.\ Across five models and twelve benchmarks, prompt‑template diversity reduces path correlation in 55 of 57 valid cells, with the strongest effect on open‑ended QA. From this observation we derive an Adaptive‑K rule: a four‑path pilot estimates correlation and selects an optimal $K^*$, preserving $96\%\sim103\%$ of the MV@$K{=}32$ accuracy on Math, QA, and NLU tasks.\
Review: The paper bridges multi‑path reasoning with channel‑combining theory, offering a theoretical justification for majority voting and a practical adaptive sampling strategy that mitigates the diminishing returns of increasing $K$.