two different agents can come up with two different prior for the same problem, they can do so only if they have different information
Sure, but agents almost always have different background information, in some cases radically different background information.
Let's say a pharma company comes out with a new drug. The company claims: "Using our specially-developed prior, which is based on our extensive background knowledge of human biochemistry, in combination with the results of our recent clinical trial, we can see that our new drug has a miraculous ability to save lives!" An outsider looks at the same data, but without the background biochemical knowledge, and concludes that the drug is actually killing people.
You can partially alleviate this problem by requiring the pharma company to submit its special prior before the trial begins. But that's not what Jaynes wanted; he wanted to claim that there exists some ideal prior that can be derived directly from the problem formulation.
Sure, but agents almost always have different background information, in some cases radically different background information.
In that case, it's the correct situation that they come up with different prior.
he wanted to claim that there exists some ideal prior that can be derived directly from the problem formulation.
Yes, but he also made a point to always include all background information in the problem formulation. He explicitly wrote so, and his formulas had a trailing term P(...|...,X) to account for this.
It might be interesting to explore what...
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