Monday, August 13, 2018

Intractable problems

In In Soviet Union, Optimization Problem Solves You, Cosma Shalizi makes a good case that the optimization problem for a national economy is more-or-less computationally intractable. This news does not come as any kind of a surprise to me.

But so what? Intractable problems are intractable. It doesn't matter if we call this or that heuristic "capitalism" or "socialism"; because we know that it is impossible to calculate what the "optimum" economy looks like, we know that neither capitalism nor central-planning communism (I refuse to call these synonyms) nor anything else is going to deliver an optimum economy.

It's worth repeating for emphasis: intractable problems are intractable: there is no way to find a solution even if it were known that a solution exists. If capitalism could solve the optimization problem, then the optimization problem would not be intractable. But it is intractable, so capitalism can't solve it any better than central-planning communism.

I really don't know much about the actually existing economies of the USSR or of the Maoist PRC. I have very little information: the East wasn't talking, and the West wasn't listening. What little information is available is so obviously biased I can't put together an historical narrative reliable enough to draw general conclusions.

But maybe we can draw some general conclusions from information theory. We can't solve the economy, but we can employ heuristics to make it good enough, and give directions for improvement. The key is, of course, feedback and a dynamic rather than a static view. We need to implement intentional inefficiency, i.e. redundancy and slack (unused capacity).

The Internet, for example, is "ideal" in a sense precisely because it is inefficient. It is inefficient, for example, to have multiple paths from Denver to San Francisco; it would be more efficient to have only one path, which was optimized to provide exactly the required throughput. Instead we have many paths, none of which operate at full capacity.

Capitalists argue that capitalism is such a feedback system, and the "anarchy of capitalism" affords precisely the required redundancy and slack. Partially granted. But capitalism is not the only possible feedback system, and the "anarchy of capitalism" is not the only way to afford redundancy and slack.

Worse yet, Marx and Lenin argue* that even in its ideal form, capitalism, while yes, a dynamic feedback-oriented system, and yes, far better than mercantilism or feudalism, is still a "bad" system, prone to destructive positive feedback (financial crises) and the tendency to monopolism, which destroys beneficial redundancy and slack. (Marx levels many other charges against capitalism, but the above are especially pertinent here.)

*You know what I mean.

I am generally agnostic at an ideological level about "mechanisms". The important differences between capitalism, socialism, and communism are not differences about methods, static or dynamic, feedback-oriented or command-oriented, etc. Static top-down methods are probably not particularly useful, since they are brittle: either exactly right or disastrously wrong. (In what little information I've seen about the economy of the USSR that I don't completely dismiss as hopelessly tendentious, Western economists argued that effective feedback systems did evolve in the supposedly rigid and inviolable Soviet central planning mechanism.)

Any time we're dealing with a heuristic, we have to ask, good enough for whom? Improving for whom? By what measures? What do we mean by "efficiency"? What are the numerator and denominator? The answers to these questions are more easily answered with algorithmic solutions: they're right there in the specification of the problem. They're harder to answer with dynamic feedback systems, because the answers often emerge from the feedback mechanism itself, and emerge in non-obvious ways. Moreover: how does the system provide enough positive feedback to grow, but enough negative feedback to not grow pathologically or self-destructively?

And I think the important differences between capitalism and socialism are that the former answers, good enough for the bourgeoisie, and the latter, good enough for the proletariat. The rest is implementation detail.

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