We argue that the phenomena of distributed responsibility, induced acceptance, and acceptance through ignorance constitute instances of imperfect delegation when tasks are delegated to computationally-driven systems. Imperfect delegation challenges human accountability. We hold that both direct public accountability via public transparency and indirect public accountability via transparency to auditors in public organizations can be both instrumentally ethically valuable and required as a matter of deontology from the principle of democratic self-government. We analyze the regulatory content of 16 guideline documents about the use of AI in the public sector, by mapping their requirements to those of our philosophical account of accountability, and conclude that while some guidelines refer processes that amount to auditing, it seems that the debate would benefit from more clarity about the nature of the entitlement of auditors and the goals of auditing, also in order to develop ethically meaningful standards with respect to which different forms of auditing can be evaluated and compared.