Abstract

Team science holds that leadership is \emph{contingent}: it helps only under specific conditions, and capable, autonomous teams may need none at all. We ask the analogous question for multi-agent LLM teams: under what \emph{measurable} conditions does process-level coordination control add value, and do those conditions match what team science predicts? Answering it takes measurement, not just accuracy: we use \emph{behavioral signatures} (majority lock-in, exploration, recovery from an incorrect round-0 consensus) and \emph{per-action ablations}, clean because each controller is an explicit action set rather than a monolithic prompt. We operationalize three classical leadership styles (transactional, transformational, situational) as controllers over a shared action vocabulary (\texttt{explore}, \texttt{revise}, \texttt{accept}, \texttt{synthesize}), holding the agent set and final aggregation fixed. Team science \citep{hackman2002leading,bass1985leadership,hersey1969management} supplies the substrate: Bass's two-component structure maps to the \texttt{accept} and \texttt{revise} actions, giving the transactional controller its decomposition. A matched controller with the same actions but an \emph{arbitrary} rule recovers no better than majority voting, so it is the theory-derived rule, not the vocabulary, that does the work. Across four task regimes and three open-weight model families on a single backend, no controller dominates by accuracy, as the contingency view predicts. Against a \emph{shared} round-0 vote, generated once and reused across conditions, transactional control matches the vote on all 12 (model, regime) combinations to within $1.3$pp, and accuracy gains appear in only two of the 36 leadership entries, situational and transformational, both on the single \texttt{llama-4-scout} social combination, where the round-0 majority is unreliable. Against the stronger flat baseline, only situational still gains ($+8$pp). A \emph{recovery-advantage} account, tested with four boundary probes, says when a controller beats plain interaction: only where the round-0 majority is unreliable, the task is recoverable, and undirected interaction does not already repair it. These conditions map onto contingency theory (leadership substitutes, path-goal redundancy, and the situational readiness gap), so a largely null accuracy result is what the theory predicts, not a failure of the controllers. We read process-level coordination control as a contingency to be measured and theory-mapped, not a leaderboard to be topped.