Arrow's theorem applies only to ordinal voting methods. Approval is not actually subject to Arrow's theorem; it's not even well-defined whether it passes the cr

Arrow's theorem applies only to ordinal voting methods. Approval is not actually subject to Arrow's theorem; it's not even well-defined whether it passes the criteria. However, there are various voting impossibility theorems inspired by Arrow which do apply to approval. Most notably, Gibbard-Satterthwaite.