Background: The health status of the Sub-Saharan African (SSA) countries is well below that of the rest of the world. Coupled with low per capita income, these countries have agreed and committed themselves to raising their health status equitable standard by addressing United Nations (UN) Sustainability Development Goal number 3 (SDG3) by 2030. Addressing SDG3 requires increased and equitable funding for universal health coverage, healthcare infrastructure, efficient resource allocation, improved priority setting, reduction in corruption, and other strategies. However, what is urgently needed to improve priority setting processes or meaningful health system reform, among other things. There is therefore a need for the exploration of the economic and non-economic (which includes social justice) explicit criteria that ought to form the normative framework for Decision Making. These explicit criteria include efficiency, burden of disease, equality (strict egalitarianism), equity, and explicit criteria. Methods: The ultimate aim was to identify explicit values/principles/criteria that can be used to formulate an ideal normative framework to be used to guide decision Making so as to improve SDG3 in SSA. We synthesized selected literature on the normative frameworks for priority setting processes in health in SSA was undertaken, and the explicit criteria which, ought to guide these frameworks were identified. The form of the Social Welfare function and its principles was identified. Results and Conclusions: The framework and its explicit criteria for priority setting in the SSA countries that ought to be adopted in order to improve their SDG3 was identified—Non-Welfarist framework. This framework allows utility, health and other important social values/attributes/principles to enter the normative SWF. It is argued that such a framework ought to be specified empirically and concurrently by the decision-makers and members of the community representatives. Community representatives ought to be recognized as legitimate claimants of the resources determined, and should therefore be allowed to have a role in specifying the arguments in the SWF and what weights to be attached to the stated arguments. This implies that the selection of options in decision-making should focus on maximizing benefit and minimizing the opportunities forgone as stated in the framework.