What Does Talking Add? The Value of Feedback in Multi-Agent Inference

In multi-agent language model systems, a decision-maker combines reports from agents with different private evidence to answer a task question. Limited report space requires each agent to select which evidence to include. The information needed for this selection may be held by another agent, leaving the reporting agent uncertain about what to preserve. A follow-up protocol addresses this issue by allowing the decision-maker to ask questions after reading the initial reports. We compare the accuracy and cost of this protocol with stronger independent reporting and sequential reporting protocols. Stronger independent reporting improves report encoding and allows local revision, while sequential reporting sends selection information from one agent to another before the receiving agent prepares a report. Each agent’s initial evidence access and the total resource limits remain unchanged across protocols. Our analysis separates accuracy loss caused by information missing from reports from failures to use information already received. Before the sender knows which evidence is needed, a report must support multiple possible needs. Earlier access to selection information can reduce what the report must preserve. Controlled routing and document-selection experiments show that stronger reports reduce the estimated accuracy advantage of follow-up. With the direction of information dependence known, sequential reporting achieves high accuracy with fewer generated tokens than follow-up. The experiments also reveal errors in preparing and reading reports, even when the report budget is sufficient to include all required information.