Digital tracing technologies are heralded as an effective way of containing SARS-CoV-2 faster than it is spreading, thereby allowing the possibility of easing draconic measures of population-wide quarantine. But existing technological proposals risk addressing the wrong problem. The proper objective is not solely to maximise the ratio of people freed from quarantine but to also ensure that the composition of the freed group is fair. We identify several factors that pose a risk for fair group composition along with an analysis of general lessons for a philosophy of technology. Policymakers, epidemiologists, and developers can use these risk factors to benchmark proposal technologies, curb the pandemic, and keep public trust.