The question of what motivates compliance with authority is critical for understanding social cooperation, state-building, inequalities in political representation and potential for development. Which authorities have the most influence over which individuals and which types of communities? What is the basis of their influence? These questions have theoretical and substantive significance. We conduct conjoint endorsement experiments that allow us to measure the basis of authority and the levels of legitimacy of different leaders across two different sub-Saharan Africa countries. The experimental arms are designed to allow us to explore whether sanctioning, coordination, or legitimacy drive individuals’ willingness to comply with leaders’ directives. We embed this experiment in the Local Governance Performance Index (LGPI), which is designed to be representative at the local level and provide community-level indicators. Doing so allows us to explore the relationship between community- and individual-level factors, the strength of different authorities in different contexts, and the factors underlying their influence. The analyses relating contextual and individual characteristics to authorities are observational, of course; nevertheless, they provide important leverage on questions regarding in what conditions different authorities can demand compliance, and over whom they have influence.