Social Welfare Function
Updated 2026-08-13
INTRODUCTION
English translation pending.
CORE DEFINITION
A social welfare function is a mathematical rule that maps the utilities of all members of society into a single measure of aggregate welfare, W = f(u1, u2, ... un). Different functions embody different ethics: utilitarian forms maximize the sum, Rawlsian forms maximize the utility of the worst-off, and egalitarian forms pursue equality. The core claim, sharpened by Arrow's impossibility theorem, is that no aggregation rule satisfies several reasonable conditions at once, so choosing a function is choosing a value position. The key condition is that the resulting optimum must not be presented as a purely technical conclusion.
SCAFFOLDING EFFECT
Reduce cognitive load
- Stakeholder mapping: name exactly who gains and who loses under each policy option. - Position disclosure: state the welfare function used and the ethic it embodies. - Value debate: put the implicit trade-offs on the table rather than hiding them.
Anchor fast decisions
Each individual's utility cannot be observed directly, so it must be estimated and then combined by a rule, and every candidate rule violates at least one reasonable demand, which Arrow's theorem demonstrates. Because the rule's output changes with its ethical assumptions, the apparent optimum is a product of the chosen function. Exposing the function therefore converts a technical calculation into an explicit value choice, which is what legitimate collective decision requires.
MINIMUM ACTION
In progress 0/1Practice this model in one real situation:
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Source support: Explicit
- en.wikipedia.orghttps://en.wikipedia.org/wiki/Social_welfare_functionverified
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