Every day, millions of administrative decisions take place in the public sector: building permits, land use, tax deductions, social welfare support, and access to healthcare, etc. When such decisions affect the rights and duties of individual citizens and/or businesses, they must meet the requirements set out in administrative law. Of those is the requirement that the body responsible for the decision must provide an explanation of the decision to the recipient. As many administrative decisions are being considered for automation through algorithmic decision-making (ADM) systems, it raises questions about what kind of explanations they need to provide. Fearing the opaqueness of the dreaded black box of these ADM systems, countless ethical guidelines have been produced, often of a very general character. Rather than adding yet another ethical consideration to what in our view is an already overcrowded ethics-based literature, we focus on a concrete legal approach, and ask: what does the legal requirement to explain a decision in public administration actually entail in regards to both human and computer-aided decision-making? We argue that, instead of pursuing a new approach to explanation, retaining the existing standard (the human standard) for explanation already enshrined in administrative law will be more meaningful and safe. To add to this we introduce what we call an ‘administrative Turing test’ which could be used to continually validate and strengthen computationally assisted decision-making, providing a benchmark on which future applications of ADM can be measured.