In recent years, local government is undergoing changes which are strongly influenced by the growing digitization of governmental operations. Key features of Digital Era Governance (DEG) appear to be displacing features of the New Public Management (NPM) and are also challenging some underlying aspects of Weberian bureaucracy in public administration. In this paper, we expand on the concepts in DEG and its successor, Essentially Digital Government (EDGE), by introducing the concept of Algorithmic Bureaucracy, which looks at the impacts of Artificial Intelligence (AI) on rationalization and the socio-technical nature of public administration. We report on a mixed-method study, which focused on how the growth of data science is changing the ways that local government works in the UK. Special emphasis is put on how algorithms can build citizen and administrator competence and deal with complexity. Algorithmic bureaucracy, like traditional bureaucracy, is impartial in its application, but can be predictably sensitive to context. Society needs to determine the ends to which it is put and how to assign accountability in this context. We find that algorithmic bureaucracy is in its infancy in local government, so there is space to develop an appropriate ethical framework to harness the technology and enhance social problem solving.