Increasingly secret, complex and inscrutable computational systems are being used to intensify existing power relations and to create new ones; in particular, they are being used to govern. To be all-things-considered morally permissible new, or newly intense, power relations must meet standards of procedural legitimacy and proper authority. This is necessary for them to protect and realise democratic values of individual liberty, relational equality, and collective self-determination. For governing power in particular to be legitimate and have proper authority, it must meet a publicity requirement: reasonably competent members of the governed community must be able to determine that they are being governed legitimately and with proper authority. The publicity requirement can be satisfied only if the powerful can explain their decision-making to members of their political community. At least some duties of explanation are therefore democratic duties. This paper first sets out the foregoing argument, then applies it to opaque computational systems, and clarifies precisely what kinds of explanations are necessary to fulfil these democratic values.
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