Relational Priors as Convergence Pressure in LLM-Based Multi-Agent Systems

Large language model-based multi-agent systems (LLM-MAS) are designed through roles, debate protocols, and aggregation rules. These choices create implicit expectations of trust, skepticism, deference, or collaboration. We make inter-agent relations explicit as signed pairwise priors, rendered in natural language and added to system prompts while keeping the task protocol fixed. Across commons governance and multi-agent debate, these priors change how readily agents coordinate or agree, a pattern we call convergence pressure. More positive relations generally improve sustainability within the GovSim relational-prior sweep and increase consensus on subjective questions. These improvements over negative relations differ from gains over no-prior prompting. On objective QA, fully positive priors usually yield lower final-answer accuracy than the no-prior baseline, and some conditions produce more frequent but less accurate consensus. Effects depend on model backbone, relation type, and topology; explicitly neutral relations also produce different outcomes from omitting relational framing. Relational priors are therefore task-specific interventions and diagnostic probes of sensitivity to social framing. Evaluate them against a no-prior baseline using the task's primary metric, report accuracy and consensus correctness alongside agreement on objective tasks, and keep no-prior prompting as the default for accuracy-centric tasks unless validation supports a relational prior.