Coordination within decentralized agent groups frequently requires reaching global consensus, but typical hierarchical approaches to reaching such decisions can be complex, slow, and not fault-tolerant. By contrast, recent studies have shown that in decentralized animal groups, a few individuals without privileged roles can guide the entire group to collective consensus on matters like travel direction. Inspired by these findings, we propose an implicit leadership algorithm for distributed multi-agent systems, which we prove reliably allows all agents to agree on a decision that can be determined by one or a few better-informed agents, through purely local sensing and interaction. The approach generalizes work on distributed consensus to cases where agents have different confidence levels in their preferred states. We present cases where informed agents share a common goal or have conflicting goals, and show how the number of informed agents and their confidence levels affects the consensus process. We further present an extension that allows for fast decision-making in a rapidly changing environment. Finally, we show how the framework can be applied to a diverse variety of applications, including mobile robot exploration, sensor network clock synchronization, and shape formation in modular robots.