LW - Aumann-agreement is common by tailcalled
Description
Welcome to The Nonlinear Library, where we use Text-to-Speech software to convert the best writing from the Rationalist and EA communities into audio. This is: Aumann-agreement is common, published by tailcalled on August 27, 2023 on LessWrong.Thank you to Justis Mills for proofreading and feedback. This post is also available on my substack.Aumann's agreement theorem is a family of theorems which say that if people trust each other and know each other's opinions, then they agree with each other. Or phrased another way, if people maintain trust with each other, then they can reach agreement. (And some variants of the theorem, which take computational factors into consideration, suggest they can do so quite rapidly.)The original proof is pretty formal and confusing, but a simpler heuristic argument is that for an honest, rational agent, the mere fact of them professing an opinion can be strong evidence to another rational agent, because if the speaker's probabilities are higher than the speaker's prior, then they must have seen corresponding evidence to justify that opinion.Some people find this confusing, and feel like it must be wrong because it doesn't apply to most disagreements. I think these people are wrong because they are not sufficiently expansive in what they think of as a disagreement. The notion of disagreement that Aumann's agreement theorem applies to is when the people assign different probabilities to events; this is a quite inclusive notion which covers many things that we don't typically think of as disagreements, including cases where one party has information about a topic and the other party has no information.My vacation in Norway relied tons on Aumann agreementsRecently, I had a vacation in Norway with my wife.In order to get there, and to get around, we needed transport. At first we disagreed with people who provided transport there, as we didn't know of many specific means of transport, only vaguely that there would be some planes and ships, without knowing which ones. But my wife had heard that there was something called the "Oslo ferry", so we Aumann-agreed that this was an option, and decided to investigate further.We disagreed with the company that provided the Oslo ferry, as we didn't know what their website is, so we asked Google, and it provided some options for what the ferry might be, and we Aumann-agreed with Google and then went investigating from there. One website we found claimed to sell tickets to the ferry; at first we disagreed with the website about when we could travel as we didn't know the times of the ferry, but then we read which times it claimed was available, and Aumann-updated to that.We also had to find some things to do in Norway. Luckily for us, some people at OpenAI had noticed that everyone had huge disagreements with the internet as nobody had really memorized the internet, and they thought that they could gain some value by resolving that disagreement, so they Aumann-agreed with the internet by stuffing it into a neural network called ChatGPT. At first, ChatGPT disagreed with us about what to visit in Norway and suggested some things we were not really interested in, but we informed it about our interests, and then it quickly Aumann-agreed with us and proposed some other things that were more interesting.One of the things we visited was a museum for an adventurer who built a raft and sailed in the ocean. Prior to visiting the museum, we had numerous disagreements with it, as e.g. we didn't know that one of the people on the raft had fallen in the ocean and had to be rescued. But the museum told us this was the case, so we Aumann-agreed to believe it. Presumably, the museum learnt about it through Aumann-agreeing with the people on the raft.One example of an erroneous Aumann agreement was with the train company Vy. They had said that they could get us a train ticket on the Bergen train, and we had Aumann-agreed with that. However, due to a storm, their train...
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