Oligarchy translates literally as "rule by the few" [1], and aristocracy as "rule by the excellent" [2]. Kakistocracy is "rule by the worst" per the featured article. So kakistocracy and aristocracy are opposites, and oligarchy describes something different: the number, not quality, of rulers.

[1] https://en.m.wikipedia.org/wiki/Oligarchy

[2] https://en.m.wikipedia.org/wiki/Aristocracy