Oh this is fascinating. This is basically correct; a high-level model space can include models which do not correspond to any possible low-level model.
One caveat: any high-level data or observations will be consistent with the true low-level model. So while there may be natural abstract objects which can’t exist, and we can talk about those objects, we shouldn’t see data supporting their existence—e.g. we shouldn’t see a real-world voting system behaving like it satisfies all of Arrow’s desiderata.
Oh this is fascinating. This is basically correct; a high-level model space can include models which do not correspond to any possible low-level model.
One caveat: any high-level data or observations will be consistent with the true low-level model. So while there may be natural abstract objects which can’t exist, and we can talk about those objects, we shouldn’t see data supporting their existence—e.g. we shouldn’t see a real-world voting system behaving like it satisfies all of Arrow’s desiderata.