Explicit health care rationing or priority-setting is the use of institutional procedures for the systematic allocation of resources within health care systems. With the establishment of priority setting systems in various countries in the past two decades, research has been conducted on their principles, methods and institutional aspects. This paper draws on the sociology of science and technology to propose an uncertainty-focused conceptual model of the relationship between knowledge practises and political processes in health care rationing. Taking a case-study approach, the paper explores the public controversy about whether dementia drugs should be available on the UK National Health Service. It shows how three aspects of the controversy - loose institutional framing, open membership and hybrid knowledge - worked together to enable the use of a 'pragmatic balance' between rules and cases. Placing this outcome within the space of possibilities suggested by the model, the paper suggests that accepting and fostering the exploration of uncertainty at the core of health care priority setting systems should provide those systems with increased social robustness.