You seem to be conflating market mechanisms with political stances.
That is possible, but the existing market has been under the reins of many a political stance and has basically obeyed the same general rules of economics, regardless of the political rules that have tried to be imposed.
In theory a market can be used to solve any computational problem, provided one finds the right rules—this is the domain of computational mechanism design, an important branch of game theory.
The rules seem to be the weakest point of the system because they parallel the restrictions that political stances have caused to be placed on existing markets. If a computational market is coupled to the external world then it is probably possible to money-pump it against the spirit of the rules.
One way that a computational market could be unintentionally (and probably unavoidably) coupled to the external market is via status and signalling. Just like gold farmers in online games can sell virtual items to people with dollars, entities within the computational market could sell reputation or other results for real money in the external market. The U.S. FDA is an example of a rudimentary research market with rules that try to develop affordable, effective drugs. Pharmaceutical companies spend their money on advertising and patent wars instead of research. When the results of the computational market have economic effects in the wider market there will almost always be ways of gaming the system to win in the real world at the expense of optimizing the computation. In the worst case, the rule-makers themselves are subverted.
I am interested in concrete proposals to avoid those issues, but to me the problem sounds a lot like the longstanding problem of market regulation. How, specifically, will computational mechanism design succeed where years of social/economic/political trial and error have failed? I’m not particularly worried about coming up with game rules in which rational economic agents would solve a hard problem; I’m worried about embedding those game rules in a functioning micro-economy subject to interference from the outside world.
I suppose there’s one scant anecdote for estimating this; cryptography research seemed to lag a decade or two behind actively suppressed/hidden government research. Granted, there was also less public interest in cryptography until the 80s or 90s, but it seems that suppression can only delay publication, not prevent it.
The real risk of suppression and exclusion both seem to be in permanently discouraging mathematicians who would otherwise make great breakthroughs, since affecting the timing of publication/discovery doesn’t seem as damaging.
I think I would be surprised if Basic Income was a less effective strategy than targeted government research funding.
Everything from logic and axiomatic foundations of mathematics to practical use of advanced theorems for computer science. What attracted me to Metamath was the idea that if I encountered a paper that was totally unintelligible to me (say Perelman’s proof of Poincaire’s conjecture or Wiles’ proof of Fermat’s Last Theorem) I could backtrack through sound definitions to concepts I already knew, and then build my understanding up from those definitions. Alas, just having a cross-reference of related definitions between various fields would be helpful. I take it that model theory is the place to look for such a cross-reference, and so that is probably the next thing I plan to study.
Practically, I realize that I don’t have enough time or patience or mental ability to slog through formal definitions all day, and so it would be nice to have something even better. A universal mathematical educator, so to speak. Although I worry that without a strong formal understanding I will miss important results/insights. So my other interest is building the kind of agent that can identify which formal insights are useful or important, which sort of naturally leads to an interest in AI and decision theory.