Democratic governments comprise a subset of a population whose goal is to produce coherent decisions that solve societal challenges while respecting the will of the people they represent. New governance frameworks represent this problem as a social network rather than as a hierarchical pyramid with centralized authority. But how should this network be structured? To investigate this question, we model the set of decisions a population must make as a satisfiability problem and the structure of information flow involved in decision-making as a social hypergraph. This allows us to consider the benefits of different governance structures, from dictatorships to direct democracy. In between these extremes, we find a regime of effective governance where decision groups are formed as needed by key stakeholders to discuss and make specific decisions. This regime of effective governance allows even incoherent or polarized populations to make coherent decisions at low coordination costs. More broadly, we present not just simulation results, but a modeling framework that can be used to explore the costs and benefits of a wide range of governance strategies using bottom-up approaches and their ability to tackle decision problems that challenge standard governments. Pre-print:https://arxiv.org/pdf/2412.03421