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I rank authorities by my confidence in the discipline as follows:
I. Mathematics, Geometry, Statistics, et al
II. Physics, Information Science, et al
III. Chemistry, Biology, Medicine, et al
IV. Astronomy, Cosmology, Geology, Climatology, Criminology, et al.
V. Anthropology, Paleontology, Archaeology, Evolution, History, et al
VI. Metaphysics, Philosophy, Psychology, Politics, et al
Nice list. Certainly your category I deserves to be ranked above the others. Math and geometry are deductive, and will always be ahead of any inductive systems in the confidence we place in their conclusions. Your last category properly deserves to be at the bottom, as those topics are riddled with subjectivity.

All the stuff in the middle, it seems to me, really depends on the quantity and quality of the evidence that we have to work with, and on the sophistication of our instruments. (I think evolution deserves to rank well ahead of archaeology, by the way.) Compared to physics, for example, archaeology seems primitive, but I suspect it's because in the field of archaeology we have so little information to go on that the resulting theories sometimes do seem more like myths than science. But it's not for lack of rationality, or application of the scientific method. The difference, in my always humble opinion, lies in the quality of the data, not in the "experimental vs. historical" disjunction.

Massive hugs.

Thank you so much for your reply! Hugs!!!

All the stuff in the middle, it seems to me, really depends on the quantity and quality of the evidence that we have to work with, and on the sophistication of our instruments.

Indeed. My ranking has nothing to do with scientists' rationality, integrity, professionalism, etc. - it has to do with the nature of the inquiry. The ability to reproduce evidence, or confirm by tools of math, diminishes the further down the list.

Consequently, the further down the list, the greater the demand for subjective analysis - and therefore, in my case, the lower my confidence in the results.