Preventive coercive measures are an increasingly common feature of the legal landscape. Examples are the preventive imprisonment of dangerous individuals after the expiration of their sentences, the involuntary commitment of dangerous individuals to mental institutions purely to protect the public, and preventive detention of suspected terrorists and the imposition of control orders on persons not charged with terrorist crimes. Such measures are based on the probability, not the certainty, of future harmful conduct and they therefore carry the danger that some people who are not dangerous will be mistakenly subjected to them. Such people are called ‘false positives’. This article explores the moral and legal complexities which surround the problem of false positives. It investigates two lines of reasoning that attempt to minimise the severity of the problem. The first line of reasoning argues that since we accept some risk of wrongful conviction in the criminal context, unreliability in the preventive context is no more worrying. The second line of reasoning argues that it is reasonable to ‘balance’ the interests of individuals who are likely to cause harm against the interests of their potential victims. Explaining why we should reject these approaches, the article argues that, as a matter of political morality, it is more important to avoid mistaken decisions to restrict liberty than mistaken decisions not to restrict liberty. It also explains the nature of the legal protections which are needed to give effect to this weighting of the competing values at stake. Finally, it sheds light on provisions prohibiting arbitrary detention and arbitrary invasions of privacy in human rights legislation, explaining how the view adopted in this article can be used to give meaning to the notion of ‘arbitrariness'.