I seriously doubt it is only polynomial even with large n, the feedbacks in an economy are impossibly complex to model, much less plan. Maybe advanced AIs will manage it some day (see the mentions of Economy 2.0 in Accelerando) but not anything near human.
According to the link, it’s O(n^3) if certain simplifying assumptions are made. (Said simplifying assumptions include that returns to scale are never positive—which isn’t too unrealistic when you’re talking about the difference between making a million diapers or a million plus one of diapers, but is unrealistic as hell when you’re talking about intellectual property or anything with large R&D costs.) However, the same conditions under which central planning actually becomes harder than O(n^3) are the same conditions under which the market allocation is inefficient, too—they’re the same kinds of conditions that tend to create monopolies, tragedy of the commons situations, etc.
I seriously doubt it is only polynomial even with large n, the feedbacks in an economy are impossibly complex to model, much less plan. Maybe advanced AIs will manage it some day (see the mentions of Economy 2.0 in Accelerando) but not anything near human.
According to the link, it’s O(n^3) if certain simplifying assumptions are made. (Said simplifying assumptions include that returns to scale are never positive—which isn’t too unrealistic when you’re talking about the difference between making a million diapers or a million plus one of diapers, but is unrealistic as hell when you’re talking about intellectual property or anything with large R&D costs.) However, the same conditions under which central planning actually becomes harder than O(n^3) are the same conditions under which the market allocation is inefficient, too—they’re the same kinds of conditions that tend to create monopolies, tragedy of the commons situations, etc.
Moved to open thread, since my point turned more general than just a response.