Sociolinguistics 2, Exercise 2: intelligibility versus labels

A purely intelligibility-based test would conclude:
  Danish and Norwegian: one language (or dialects of one), because they are
  largely mutually intelligible.
  Mandarin and Cantonese: separate languages, because they are mutually
  unintelligible.

The source reports the opposite for both:
  Danish and Norwegian count as separate languages by the sociolinguistic
  test of shared linguistic authority.
  Mandarin and Cantonese are often called dialects in China despite their
  mutual unintelligibility.

The mismatch shows that the label follows status, standardisation and
politics (the source's Weinreich saying: "A language is a dialect with an army
and navy"), not intelligibility alone.