Relational Theory of Status Hierarchy: An Extension of Gould's Model to Incorporate Multidimensional Choices

Abstract

Social status hierarchy is a prominent topic in sociology, but a complete theoretical understanding of its process has been lacking. Using game theory and social network theory, Gould showed that status hierarchy can be considered as a type of equilibrium wherein players assign attachments to other players depending on their qualities. However, Gould’s model unrealistically gives limitless attachment resources to each player. We improve Gould’s model by incorporating multidimensional choices that consider resource constraints, including factors of individual quality, social reference, and reciprocity. We find that an individual’s status is determined by the individual’s relative quality in the complete social network (in contrast to Gould’s model, where an individual’s status is dyadically determined). We also demonstrate by agent-based simulation that our model can be based on bounded-rational not hyper-rational players and that it thus has wide applicability to a variety of real world situations. Finally we find that social influence does not always amplify the inequality in the hierarchy, as Gould claimed. In fact, social influence can reduce the inequality in the hierarchy where strong reciprocity conditions are present.