say-so vs imperium

say-so and imperium both are nouns.

Word	Noun	Adjective	Verb	Adverb
say-so	Yes	No	No	No
imperium	Yes	No	No	No

As nouns, imperium is a hyponym of say-so; that is, imperium is a word with a more specific, narrower meaning than say-so:

Other hyponyms of say-so include power of appointment, carte blanche, command, lordship, muscle, sovereignty.

say-so (noun)	imperium (noun)
the power or right to give orders or make decisions	supreme authority; absolute dominion
an authoritative declaration	the domain ruled by an emperor or empress; the region over which imperial dominion is exercised
one chap's arbitrary assertion