To whom it may concern:
This thread is for the discussion of Less Wrong topics that have not appeared in recent posts. If a discussion gets unwieldy, celebrate by turning it into a top-level post.
(After the critical success of part II, and the strong box office sales of part III in spite of mixed reviews, will part IV finally see the June Open Thread jump the shark?)
There's nothing mysterious about it as far as I can tell, it's "just math".
Give me a six-sided die and I'll compute the probability of it coming up 4 as 1/6. This simple exercise can become more complicated in one of two ways. You can ask me to compute the probability of a more complex event, e.g. "three even numbers in a row". This still has an exact answer.
The other complication is if the die is loaded. One way I might find out how that affects its single-throw probabilities is by throwing it a large number of times, but conceivably I can also X-ray the die, find out how its mass is distributed, and deduce from that how the single-throw probabilities differ. (Offhand I'd say that faces closer to the center of mass of the die are more likely to come up, but perhaps the calculation is more interesting than that.)
In the case of Elbonia vs Ruritania, the other guy has some information that you don't, perhaps for instance the transcript of an intercepted conversation between the Elbonian ruler and a nearby power assuring the former of their support against any unwarranted Ruritanian aggression: they think the war is more plausible given this information.
Further, if you agreed with that person in all other respects, i.e. if his derivation of the probability for war given all other relevant information was also 0.3 absent the interception, and you agreed on how verbal information translated into numbers, then you would have no choice but to also accept the final figure of 0.4 conditioning on the interception. Bayesian probability is presented as an exact system of inference (and Jaynes is pretty convincing on this point, I should add).
I agree about Jaynes and the exactness of Bayesian inference. (I haven't read his Probability Theory fully, but I should definitely get to it sometime. I did got through the opening chapters however, and it's indeed mighty convincing.) Yet, I honestly don't see how either Jaynes or your comments answer my question in full, though I seen no significant disagreement with what you've written. Let me try rephrasing my question once more.
In natural sciences, when you characterize some quantity with a number, this number must make sense in some empirical way, te... (read more)