The law of likelihood says that any reasonable answer to the question “When is hypothesis A more likely than hypothesis B” (see Royall’s three questions) must be answered in terms of the likelihood ratio.
In particular, if are the distributions posited by hypothesis and respectively, then we have more evidence for precisely when the likelihood ratio is greater than one, and the magnitude of the likelihood measures the strength of that evidence.
As stated by Hacking and Royall (for discrete spaces):
Law of likelihood: If hypothesis A implies that the probability that a random variable takes the value is , while hypothesis implies that the probability is then the observation is evidence supporting over if and only if , and the likelihood ratio, measures the strength of that evidence
See Royall’s book Statistical Evidence: A Likelihood Paradigm.
The law of likelihood is stronger than the likelihood principle.