Using the 2004 Rural Development Initiative data, 99 communities are compared. Three varieties of social capital and ten other constructs serve as dependent variables. The social capital forms are within group, between group, and out-bridging. The dependent qualities are homogeneity, us-versus-them, embeddedness, selectorate, trusting attitude, cohesiveness, contentment, relational rationality, satisfaction with public services and satisfaction with government services. The four forms of cardinality are level cardinality, bijective cardinality, injective cardinality and composite cardinality. An analytic paradigm employing lattices and network analysis is developed to analyze hypotheses. I also address a confusion that grows from sociology investigating groups and group interaction with an ontologically individualist focus. In this dissertation I prove, using the logic of sets pursuant with set theory, that the application of methodological individualism is a mistake. I prove instead that decision-making is embedded in the social order and that a relational perspective employing methodological holism can be achieved.