What is the difference between social choice function and social welfare function? I am trying to understand a shard proof on Arrow's Impossibility Theorem and Gibbard-Satterthwaite Theorem. I stumbled upon these 2 different functions, and I cannot understand the difference between them: f:L^n→A - social choice function F:L^n->L* - social welfare function

Assume that finite set of alternatives are a,b and c.

A social choice function can have one single output which can be a or b or c.

A social welfare function can have any ranking as output such as $a