Governing common-pool resources requires agents to develop enduring strategies through cooperation and self-governance to avoid collective failure. While foundation models have shown potential for cooperation in these settings, existing multi-agent research provides little insight into whether structured leadership and election mechanisms can improve collective decision making. The lack of such a critical organizational feature ubiquitous in human society presents a significant shortcoming of the current methods. In this work we aim to directly address whether leadership and elections can support improved social welfare and cooperation through multi-agent simulation with LLMs. We present our open-source framework that simulates leadership through elected personas and candidate-driven agendas and carry out an empirical study of LLMs under controlled governance conditions. Our experiments demonstrate that having elected leadership improves social welfare scores by 55.4% and survival time by 128.6% across a range of high performing LLMs. Through the construction of an agent social graph we compute centrality metrics to assess the social influence of leader personas and also analyze rhetorical and cooperative tendencies revealed through a sentiment analysis on leader utterances. This work lays the foundation for further study of election mechanisms in multi-agent systems toward navigating complex social dilemmas.