Three Toed Sloth has a nice exposition on the difficulties of optimizing an economy, including the best explanation of convex optimization ever:
If plan A calls for 10,000 diapers and 2,000 towels, and plan B calls for 2,000 diapers and 10,000 towels, we could do half of plan A and half of plan B, make 6,000 diapers and 6,000 towels, and not run up against the constraints.
Maybe add "[Link]" to the title to appease the people who get angry about that sort of stuff.
That planning is not a viable alternative to capitalism (as opposed to a tool within it) should disturb even capitalism's most ardent partisans. It means that their system faces no competition, nor even any plausible threat of competition. Those partisans themselves should be able to say what will happen then: the masters of the system, will be tempted, and more than tempted, to claim more and more of what it produces as monopoly rents. This does not end happily.
A consideration like this seems to demand a refinement of the concept of FAI. To what extent is an AI that puts itself on the top of the existing economic order and extracts rents (maybe more, maybe less than the folks currently on top) friendly or unfriendly? Given the complexity and information-gathering constraints involved in economic planning, an we expect an AI to aim for anything more/better than this?
it says nothing about whether it is friendly or unfriendly. If it extracts rents from things humans don't actually want in reflective equilibrium and channels it into things they do want it is friendly, vice versa unfriendly.
it is also phenomenally unlikely that the most powerful optimization an AI will be able to do is piggyback our financial system.
Essay is highly recommended; I've started Red Plenty after reading it, and am a little disappointed it's fiction rather than a nonfiction treatment of linear optimization. :)
The author of the book Shalizi is discussing comments in the giant (154+) comment thread for Shalizi's essay, incidentally: http://crookedtimber.org/2012/05/30/in-soviet-union-optimization-problem-solves-you/comment-page-1/
After seeing this post, I read "Red Plenty" ( a sort-of novel about the failure of central planning in the USSR which the article references).
SPOILERS(?!) about Soviet planning and the novel from here onwards:
Though the tragedy here is mainly treated as caused by the intervention (or lack thereof) of bureaucrats, the work moved me to view communism in a sympathetic way I hadn't before: Khrushchev (as presented in the novel) wanted a post-scarcity society. He wanted to outcompete the West on its own terms of goods and standard of living, and use central planning to do it.
Kantorovich's desire to optimize and the feeling of momentum and energy that Russia's intelligentsia were presented as having was infectious, and I found myself (even knowing the inevitable end) lamenting each loss of efficiency, each creation of perverse incentives, and hoping against hope that Kantorovich would be allowed to merely try his ideas without being stymied by rent-seeking incompetents (i.e., Brezhnev) who did nothing simply to stay in power. Lysenko was another (unseen) villain through his perversion of biology and its effect on one of the main characters.
The economic calculation problem was noted as early as the 1850s. In contrast, the "Communist Manifesto" was published in 1848. The economic calculation problem does seem to point out a hole in the bucket of central planning. A leaky bucket can still carry some water, of course. A review of the history of the theory and an explanation of the theory can be found in "Posing the Problem: The Impossibility of Economic Calculation under Socialism" by David Ramsay Steele [http://www.la-articles.org.uk/ec.htm]
I saw this on Crooked Timber, and I have to say, it's one of the best blog posts I've read in a long time. Not just the thoughtful application of complexity theory, but there's a whole load of interesting political (gasp!) stuff in there.
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.
it says nothing about whether it is friendly or unfriendly. If it extracts rents from things humans don't actually want in reflective equilibrium and channels it into things they do want it is friendly, vice versa unfriendly.
it is also phenomenally unlikely that the most powerful optimization an AI will be able to do is piggyback our financial system.