It seems to me like voting the most powerful into office can't be a feature of an oligarchy, by definition. Am I misunderstanding the Sparta government?
/u/Iphikrates has answered a very similar question that you might find useful: [Why isn't Sparta considered a democracy?] (https://www.reddit.com/r/AskHistorians/comments/6zw3fs/why_isnt_sparta_considered_a_democracy/dmytzjb/)