This article investigates the existing international hierarchy employing expert survey as its primary method. 'Authority hierarchy' and 'power status hierarchy,' the two existing research traditions of hierarchy studies, are briefly introduced. We demonstrate a gap between basic research on power status, emphasizing its social nature, and applied case studies, primarily relying on purely material indicators of a country's capabilities, such as the GDP and CINC. In times of rapid hierarchical shifts, there is a need for a more nuanced and holistic approach. The article suggests placing hierarchy studies onto the ontological foundation of Niklas Luhmann's Differentiation Theory to overcome these problems. We trace the international society's segmentary differentiation, stratificatory differentiation (status hierarchy), and functional differentiation (specialization). The paper argues that the functional roles of states and their positions in the international hierarchy are interconnected. The hierarchy of states' roles, resulting from functional differentiation, is understood in terms of authority hierarchy. In order to lay the ground for further research, three valuable insights of states in the international hierarchy. Firstly, we categorize 26 countries as belonging to one of the power status categories (small power, middle power, great power, superpower) as of autumn 2021 based on the survey results. We calculate indices operationalizing power, roles, public goods provision, and revisionism for the states in the survey. Secondly, the paper presents experts' evaluations of the importance of various valued attributes (such as the size of the economy, military might, international prestige, autonomy, etc.) for different power status categories. Thirdly, we suggest a novel approach linking a country's position in the international hierarchy to its functional roles. We use correlation analysis to test the hypothesis and compare the roles index to other popular power status indicators.