Based on privacy calculus theory, we derive hypotheses on the role of perceived usefulness and privacy risks of artificial intelligence (AI) in public services. In a representative vignette experiment (n = 1,048), we asked citizens whether they would download a mobile app to interact in an AI-driven public service. Despite general concerns about privacy, we find that citizens are not susceptible to the amount of personal information they must share, nor to a more anthropomorphic interface. Our results confirm the privacy paradox, which we frame in the literature on the government’s role to safeguard ethical principles, including citizens’ privacy.