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ciphergoth comments on What is Bayesianism? - Less Wrong
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Can you be clearer? Log likelihood ratios do add up, so long as the independence criterion is satisfied (ie so long as P(E_2|H_x) = P(E_2|E_1,H_x) for each H_x).
As long as there are only two H_x, mind you. They no longer add up when you have three hypotheses or more.
Indeed - though I find it very hard to hang on to my intuitive grasp of this!
Here is the post on information theory I said I would write:
http://lesswrong.com/lw/1y9/information_theory_and_the_symmetry_of_updating/
It explains "mutual information", i.e. "informational evidence", which can be added up over as many independent events as you like. Hopefully this will have restorative effects for your intuition!
Don't worry, I have an information theory post coming up that will fix all of this :)