Tang & van Heuven 2009 "Mutual intelligibility of Chinese dialects experimentally tested" address this kind of question experimentally for Chinese dialects. They do not come up with percentages like you're looking for, but in principle such a computation could be done, though you also have to decide "in what respect" (words? sentences?). Interestingly, they they discovered that e.g. Xiamen is only 39% mutually intelligible with Xiamen, though Chaozhou is 68% mutually intelligible with Chaozhou. The worst case seems to be Xiamen - Changsha, which are only 12% mutually intelligible for word-identification. The study at least provides a methodology for objectively answering the question.
There is a book by Delsing & Lundin-Åkesson which studies mutual intelligibility of Norwegian, Swedish and Danisk among the young. Sect. 4.2.1 starts to present experimental results (though I confess that I didn't work through the methodology: they found that the Danish video test was the easiest and the Norwegian one was the hardest (the Norwegians understood the Swedish better than they understood the Norwegian).
There is, additionally, the large problem that people don't speak the literary standards of Norwegian. I understand that Skrutvold dialect of Norwegian may be harder to understand for a speaker of Finmark Norwegian, so the test would presumably be of e.g. Oslo Norwegian vs. Stockholm Swedish.
