Social Welfare Functions

When evaluating public policy, a government must decide how to balance the competing needs of its citizens. To do this mathematically, economists use a Social Welfare Function (SWF).

An SWF is a mathematical framework that ranks different societal states. It defines what a "good" outcome looks like by taking the individual wellbeing scores of the population and aggregating them into a single metric of national success.

There is no universally agreed-upon SWF. The choice of function is inherently political and ethical, dictating whether a government prioritises overall growth, equality, or the protection of the vulnerable.

The two traditional approaches to this aggregation are:

1. Benthamite Aggregation: Which seeks to maximise the total sum of wellbeing.
2. Rawlsian Justice: Which seeks to maximise the wellbeing of the absolute worst-off.

Before exploring advanced models, we must understand the mechanics and limitations of these two foundational frameworks.