Arrow’s theorem doesn’t apply to rating systems like approval or range voting. However, Gibbard-Satterthwaite still holds. It holds more intensely if anything since agents have more ways to lie. Now you have to worry about someone saying their favorite is ten times better than their second favorite rather than just three times better in addition to lying about the order.
My cursory understanding is that none of these proofs apply to rating systems, only ranking systems, correct?
Arrow’s theorem doesn’t apply to rating systems like approval or range voting. However, Gibbard-Satterthwaite still holds. It holds more intensely if anything since agents have more ways to lie. Now you have to worry about someone saying their favorite is ten times better than their second favorite rather than just three times better in addition to lying about the order.