Sentence 1: While authoritarian regimes can make war without the consent of the governed--as any number of democratic enthusiasts have pointed out--they can also make peace without consulting the voters.

Sentence 2: Authoritarian leaders are unable to make war or peace without first consulting their voters.
Is this second sentence entailed by the first?

Answer: no

Sentence 1: As any 10-year-old knows (and game theorists can now elaborately prove), three-person secrets are particularly troublesome in this regard, because nobody can ever pinpoint which of the other two might have cheated.

Sentence 2: Three-person secrets have been elaborately proven by game theorists to be particularly troublesome.
Is this second sentence entailed by the first?

Answer: yes

Sentence 1: you need metal instead of plastic

Sentence 2: Metal is better than plastic for your purpose.
Is this second sentence entailed by the first?

Answer:
it is not possible to tell