The integration of artificial intelligence (AI) into public sector decision-making processes signifies a paradigm shift with profound implications for power dynamics. This chapter uncovers the ways in which the (partial) automation of decision-making, facilitated by AI, redistributes power in public administrations, with particular emphasis on civil servants' discretionary power. By grounding our analysis in the fundamental concepts of power, we aim to propose a typological framework that identifies and explores four types of power shifts: upward, horizontal, outward and reinforcement. Each type encapsulates a unique set of changes induced by AI, from the centralisation of authority and standardisation of processes to the empowerment of technical experts. This conceptual exposition not only encourages academic discourse but also provides actionable insights for policymakers navigating the complexities of AI adoption in decision-making. The chapter underscores the importance of considering the ramifications of these power shifts on accountability, transparency and democratic values. It concludes by highlighting the need for empirical research to validate and expand on the proposed framework, with the goal of informing the development of responsible and equitable AI adoption in the public sector.