arXiv:2604.17139v2 Announce Type: replace-cross Abstract: Majority voting offers a simple way to combine answers from multiple large language model (LLM) agents. When a majority follows instructions favoring the same incorrect answer, however, agreement reinforces the error. We call this failure the "consensus trap": a minority may identify the error, yet its reasoning cannot change a vote over completed answers. We introduce chunk-interleaved Round-Robin (RR) collaboration, in which agents take turns extending one unfinished reasoning trajectory. A minority of agents with correct reasoning can insert corrections that subsequent speakers read before the answer is complete. RRMaj combines several such trajectories by a final vote. We characterize a majority barrier for outcome-level voting over final answer labels and derive a local sufficient condition for expected progress when the minority's cumulative corrections outweigh opposing corrupted updates. Across model families and verifiable reasoning benchmarks, RRMaj substantially improves accuracy under majority corruption while retaining comparable average performance under minority corruption in the main advisory-instruction setting. RR also strengthens full-response debate. Scoring the shared reasoning between turns shows that, on average, continuations from uncorrupted agents increase support for the correct answer over the incorrect target. Parallel local serving adds modest latency in the measured deployment. These findings show how language shared during reasoning, and the timing of that exchange, can help a minority correct a group's answer.