This is similar to some stuff Sam was working on. I still personally suspect an equivalence to LL, but haven’t yet made it work.
This post also sorta touches on the problem of synchronous time in logical induction, which you and I discussed via private chat. A better understanding of time in logical induction / radical probabilism would seem useful here.
Yup, that was exactly the chat which got me thinking about the production-of-true-contracts thing. If a production approach worked, then ideally we could remove the deductive process entirely from the LI construction. Then the whole thing would look a lot more like standard economic models, and it should be straightforward to generalize to multiple decentralized markets with arbitrage between them.
Competing cross-market arbitrageurs would bound divergence between prices in different markets—it only takes a small price difference for an arbitrageur to move large quantities from one market to another. As a result, prices of all markets end up (nearly) identical, and the whole thing acts as a single market. The more general principle at work here: two markets in equilibrium act like a single market.
Mathematically: each market mechanism is computing a fixed point, and simultaneously solving two coupled fixed-point problems is equivalent to solving a single fixed-point problem.
In principle, this would also work for normal LI, but the deductive process would still be a single monolithic interface to the rest of the world, so we wouldn’t really gain much from it. With truth-producers, the producers can be spread across sub-markets.
This is similar to some stuff Sam was working on. I still personally suspect an equivalence to LL, but haven’t yet made it work.
This post also sorta touches on the problem of synchronous time in logical induction, which you and I discussed via private chat. A better understanding of time in logical induction / radical probabilism would seem useful here.
Yup, that was exactly the chat which got me thinking about the production-of-true-contracts thing. If a production approach worked, then ideally we could remove the deductive process entirely from the LI construction. Then the whole thing would look a lot more like standard economic models, and it should be straightforward to generalize to multiple decentralized markets with arbitrage between them.
Oh hmmm. How would the generalization work?
Competing cross-market arbitrageurs would bound divergence between prices in different markets—it only takes a small price difference for an arbitrageur to move large quantities from one market to another. As a result, prices of all markets end up (nearly) identical, and the whole thing acts as a single market. The more general principle at work here: two markets in equilibrium act like a single market.
Mathematically: each market mechanism is computing a fixed point, and simultaneously solving two coupled fixed-point problems is equivalent to solving a single fixed-point problem.
In principle, this would also work for normal LI, but the deductive process would still be a single monolithic interface to the rest of the world, so we wouldn’t really gain much from it. With truth-producers, the producers can be spread across sub-markets.