While data driven technologies, and notably AI, are promised to disruptively revolutionize fields as e.g. finance, law, insurance, HR, communication, transportation, political actors are remarkably silent on the implications of growing use of data in decision-making. The lack of politicization of AI is problematic. While individuals are disengaged and apathetic in safeguarding their data rights, the privatization of traditionally public law functions proceeds in many different domains based on data extraction by private actors. However, many choices currently made on how data is being used is normative in nature and will change the way the societies function, thus warrants some oversight and broader debate. This paper examines different avenues presented in literature, beyond user-centric approaches from the EU data protection and consumer laws, for public oversight of how data is used in algorithmic governance and bringing the society into the decision-making loop.