Can you summarise this series of posts as a straightforward mathematical theorem? As someone with a mathematical background, I would find that a lot easier to grasp than this expanse of text. At the moment, I can’t tell whether you are writing an exposition of the concepts, hypotheses and reasoning of the Utility Theorem, or doing something different.
Well, I’m not really doing it from an axiomatic perspective, as such, but basically I’m doing a “avoiding being stupid, that is, avoiding automatically losing and such, more or less uniquely leads to Bayesian decision theory”
ie “if an agent isn’t acting in accordance with decision theory, they’re going to be doing something stupid sooner or later”. I’m trying to construct decision theory from this perspective. The basic notions I’m working with are things like Dutch Book arguments and Stephen Omohundro’s vulnerability arguments. But I’m filling in bits that I personally had to struggle with, had to go “but wait, what about...?” until I eventually worked out what I felt to be the missing bits.
That’s my basic overall intent here. “Intro to decision theory, or, intro to why decision theory is the Right Way”. It sure seems though, unfortunately, like I’m not doing that good of a job at it presentation wise, but at least it may be useful as reference material to someone.
Can you summarise this series of posts as a straightforward mathematical theorem? As someone with a mathematical background, I would find that a lot easier to grasp than this expanse of text. At the moment, I can’t tell whether you are writing an exposition of the concepts, hypotheses and reasoning of the Utility Theorem, or doing something different.
Well, I’m not really doing it from an axiomatic perspective, as such, but basically I’m doing a “avoiding being stupid, that is, avoiding automatically losing and such, more or less uniquely leads to Bayesian decision theory”
ie “if an agent isn’t acting in accordance with decision theory, they’re going to be doing something stupid sooner or later”. I’m trying to construct decision theory from this perspective. The basic notions I’m working with are things like Dutch Book arguments and Stephen Omohundro’s vulnerability arguments. But I’m filling in bits that I personally had to struggle with, had to go “but wait, what about...?” until I eventually worked out what I felt to be the missing bits.
That’s my basic overall intent here. “Intro to decision theory, or, intro to why decision theory is the Right Way”. It sure seems though, unfortunately, like I’m not doing that good of a job at it presentation wise, but at least it may be useful as reference material to someone.