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Vladimir_Nesov comments on A note on the description complexity of physical theories - Less Wrong
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Yes. As you said, simpler theories have certain advantages over complex theories, such as possibility of deeper understanding of what's going on. Of course, in that case we shouldn't exactly optimize K-complexity of their presentation, we should optimize informal notion of simplicity or ease of understanding. But complexity of specification is probably useful evidence for those other metrics that are actually useful.
The error related to your preceding post would be to talk about varying probability of differently presented equivalent theories, but I don't remember that happening.
Yeah, I guess the preceding post needs some obvious amendments in light of this post (though the general point still stands). I hope people are smart enough to see them anyway.
I just don't understand what sense it makes for a perfect Bayesian to distinguish between equivalent theories. Is it still honestly about "degrees of belief", or is it now about those other informal properties that you list?
No sense. It's a correct thing to do if depth of understanding of these theories is valuable and one is not logically omnipotent, but using complexity-leading-to-improbability to justify this principle would be cargo cult Bayesianism.
The prior probability of a simple explanation is inherently greater than the prior probability of a complex explanation.
If all evidence/observation confirm both explanations equally, then the simple explanation still is on the lead: because it started out with a higher prior probability.