arXiv:2611.07140v1 Announce Type: new Abstract: Teams increasingly build software from cooperating large language model (LLM) agents, often assuming more agents mean more reliability. Yet the usual evidence, average benchmark accuracy, ignores the input mix a deployed system meets and the rule merging the agents' answers. Building on HIP-LLM, a hierarchical imprecise-probability assessment of single LLMs, we propose a framework combining it with a Bayesian network of the system's failure logic for multi-agent systems. Agent failure-probability intervals propagate through this network, where the combining rule can itself fail, into a reliability envelope showing which evidence limits it. In a pipeline extracting regulated chemical-hazard statements, majority voting over three models protected against the weakest but did not clearly exceed the best, and a voter failing on 5\% of demands would largely erase its advantage over the middle model. More agents yield a more defensible reliability claim, not automatically a more reliable system.