Wrong but Useful: Trajectory Value Beyond Answer Correctness in Multi-Agent Messages

2026-08-14

AI Summary

This study addresses the limitation of filtering messages solely by answer correctness in multi-agent reasoning. We propose the concept of trajectory value and a dhd quantification protocol to evaluate message utility beyond accuracy. Through controlled replay experiments and statistical testing, we demonstrate that over 40% of incorrect messages contain valid reasoning cues, and that retaining complete erroneous trajectories enhances subsequent reasoning performance more effectively than isolated correct answers. These findings reveal the auxiliary value of erroneous information, providing new metrics and reusable labels for agent communication filtering that transcend simple correctness. Consequently, this work significantly optimizes collaborative efficiency in multi-agent systems by leveraging the latent informational content within failed reasoning paths.

Abstract

Multi-agent reasoning systems often use agreement, confidence, or automated scores to decide which messages should shape a final answer. Such filtering assumes that a message likely to be correct is also worth keeping. Yet a wrong answer can contain a useful decomposition, constraint, or scientific principle. We test this distinction with Diverse Hypothesis Deliberation (DHD), a controlled measurement protocol that caches five independently generated messages and replays the same downstream solver, called the integrator, with each message available or hidden. The replay comparison measures a message's trajectory value: whether making the message available helps or harms subsequent reasoning. Across five mathematics and science benchmarks and two openly available model families, gpt-oss-120b and gemma-4-31B-it, wrong-helpful messages appear in every benchmark-model combination. Among wrong-answer messages that change final correctness, more than four in ten changes are helpful in each model. Controlled repeats show that the number of repeatable message effects is unlikely to arise from replay variation alone (p=0.0002). A focused intervention on repeatable wrong-helpful messages finds that the complete message works best, while retaining its reasoning preserves more success than retaining only its answer; the source of the complete-message advantage remains open. Within the same problem, repeated trajectory-value evidence also identifies a better keep-or-remove choice than answer correctness alone. Answer correctness is therefore informative but does not determine trajectory value. DHD measures this missing property and produces reusable labels for learning when agents should listen.

Problem

• Multi-agent reasoning
• Trajectory value
• Message filtering
• Answer correctness
• Wrong but useful

Innovation

• Trajectory Value
• Diverse Hypothesis Deliberation
• Wrong but Useful
• Multi-Agent Reasoning
• Message Filtering