In Soviet Union, Optimization Problem Solves You
More on this later. In the meantime, read it!
Saturday, August 11, 2018
3 comments:
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I haven't finished reading the article yet, but the introduction was very interesting, and I looked up Red Plenty to better understand what it was talking about. Scott Alexander (although I typically don't like him) had a good review of the book, and I thought I'd bring your attention to it. Maybe the Crooked Timber article hits upon the same themes--I guess I'll find out.
ReplyDeleteBased on my limited knowledge of linear programming, it seems like it would have great difficulty producing mixed solutions. For example, consider a toy problem where it costs some labor to produce food, and some labor to produce water. If the objective function is simply a*food+b*water, then the optimal solution is to allocate all labor to one or the other, depending on which one is more efficient. If we wanted to produce a solution where both food and water are produced, it's necessary to have a nonlinear objective function, even for this simple problem.
ReplyDeleteShalizi does mention a solution, I think: Kantorovich's idea of maximizing the production of a "given assortment". But I don't think that works, because picking the correct assortment is basically as difficult as solving the nonlinear problem.
I'm not trying to point out any great flaw in Shalizi's analysis, it's more like, this is a thing that I'm not sure I understand correctly. Anyways, thanks for the link, Larry!
Just as a technical note, the objective function itself doesn't need to be linear, only the production functions need to be linear.
ReplyDeleteOverall, the thrust of the article agrees with my economics education.