Public health communications are an everyday occurrence. Notwithstanding the frequency of these communications, compliance with them and the recommendations they contain is often limited. In this chapter, it is argued that one of the reasons for poor compliance is the failure on the part of experts to construct public health messages that accord with the rational resources of the public. For this to be achieved, experts must develop a better appreciation of the reasoning strategies that lay people use to assess risks to their health. This chapter presents an extended theoretical discussion of how one set of strategies in particular, a group of cognitive heuristics based on the informal fallacies, has the potential to facilitate decisionmaking about public health issues (Cummings, 2014a(Cummings, , 2015a).Among the informal fallacies, the argument from ignorance plays a particularly central role in public health communication. A comparative analysis is undertaken of the use of this argument in the public health communications issued by the Department of Health in Hong Kong and Public Health England in the UK. It is argued that there are qualitative differences in the use of the argument from ignorance across these two contexts. These differences influence the way in which the argument is rationally evaluated in these two public health contexts. Specifically, the public in Hong Kong is encouraged to reflect on epistemic conditions that are integral to the rational warrant of this argument. These conditions are less often acknowledged by public health agencies in the UK. Greater rational evaluation of these conditions, it is argued, leads to better decision-making in matters relating to public health.