1. The level of welfare in an economy or society expressed as a function of economic variables. This is the Bergson–Samuelson sense. Social welfare can be expressed as a function W(X₁,…,X_n) of the aggregate consumption levels X_i of goods i = 1,…,n. Alternatively, an individualistic social welfare function is a function of individual utility levels. If there are H consumers in the economy, then an individualistic social welfare function is written W(U¹,…,U^H), where U^h is the utility of h. Two special cases are the Rawlsian social welfare function W = min{U^h} and the utilitarian social welfare function W = Σ‎U^h. These functions capture different philosophies concerning the desirability of equity in distribution.

2. A process for aggregating individual preferences into social preferences. This is the Arrow sense. Arrow’s impossibility theorem addresses the difficulties of finding an acceptable aggregation process that works in all circumstances.