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The trick is in the word "value".
If you play some motte-and-bailey around it, you could redefine "value" to mean "that, which is maximized by the free market", and then prove that free market indeed maximizes value. I expect that most pro-market answers you will get at most places will be a variant of this.
The question is, how closely related is such definition to our intuitions about value, i.e. what we actually mean by "value". That is tricky, because human intuitions are in general unreliable (e.g. likely to change if you describe the same situation using different words), inconsistent, implemented on a broken hardware, etc. But of course that doesn't give us a license to redefine words arbitrarily, so... as the saying goes, it's complicated.
You are correct about the similarity between free market and PageRank. Free market is recursive -- you can only gain money by selling to people who have money, who in turn gained that money by selling to people who had money, etc. If you are a starving person with no money and nothing to sell, well, sucks to be you; there may be tons of food on the market, but no way to sell it to you, unless someone gives you some money first.
Money is not the same as value, though, and that is one of the places where the whole process is grounded in something other than recursion. Value can be created by work, or by selling or renting resources you have.
Also, economical value can be brought from outside of the free-market system. For example, an African warlord can extract resources locally using murder or slave work, but then can exchange those resources at the international free market for something else. What I am hinting at here is that even if you would in abstractly prove that "free market benefits all participants", that doesn't necessarily mean it benefits all humans, because some "participants" at the market are e.g. slave owners, and the "benefits" for them include the ability to exploit their slaves more safely and easily. That doesn't necessarily imply that it benefits the slaves, too; it may sometimes be the other way round. (Lenin would say: "Those naive libertarians in Silicon Valley keep inventing and selling on free market a cheaper and stronger rope with which we can now hang more people, mwa-ha-ha-ha!")
Speaking about human values, we have terminal and instrumental values, and the instrumental values are also recursive by nature.
So...
Seems to me that the recursive nature could be a red herring. Markets are recursive. Instrumental values are recursive. Maybe these things actually match each other well. Perhaps we should focus on (1) whether the non-recursive parts also match each other; and if there is a difference, (2) whether the recursive parts amplify the difference.
(I do have some opinions on that, but this comment is already too long, and contains important parts I wouldn't want to get ignored just because I write something controversial afterwards.)
I guess my point was that "sucks to be you" situations don't just happen when you have nothing of value to sell, as libertarian-minded folks (like Lumifer in this thread) seem to believe. It also happens when you have stuff to sell, but the folks who would normally buy it from you can't pay you enough t... (read more)