The way in which we describe processes of automation, the digital society and the technology companies that deliver many of its services carry implicit and sometimes contradicting values and ideas about the society envisioned. In this paper, we are interested in unfolding some of the metaphors that guide political discourses on digitalisation in Denmark, particularly those related to the nexus between the welfare state and the market. We propose that metaphorical analysis of policy documents serves to tease out and confront the implicit values and tensions related to how welfare ideologies are reconciled with market logics. This carries important messages about the Danish government’s imaginary of digitalisation and citizens, such as which role citizens are expected to play vis-à-vis digital services and welfare provisions. This paper argues that in contrast to the EU’s declared goal of human-centric digitalisation, the Danish government relies on metaphors that are technology-centric rather than human-centric.