Algorithmic decision-making is neither a recent phenomenon nor one necessarily associated with artificial intelligence (AI), though advances in AI are increasingly resulting in what were heretofore human decisions being taken over by, or becoming dependent on, algorithms and technologies like machine learning. Such developments promise many potential benefits, but are not without certain risks. These risks are not always well understood. It is not just a question of machines making mistakes; it is the embedding of values, biases and prejudices in software which can discriminate against both individuals and groups in society. Such biases are often hard either to detect or prove, particularly where there are problems with transparency and accountability and where such systems are outsourced to the private sector. Consequently, being able to detect and categorise these risks is essential in order to develop a systematic and calibrated response. This paper proposes a simple taxonomy of decision-making algorithms in the public sector and uses this to build a risk management framework with a number of components including an accountability structure and regulatory governance. This framework is designed to assist scholars and practitioners interested in ensuring structured accountability and legal regulation of AI in the public sphere.