As you wrote: > china to say (but do know they have billionaires and hedge funds, à la the Quantum Fund), USSR had its nomenklatura (several of whom went on to literally be called oligarchs in the FSU),
I believed that your thoughts were on this "rule by the rich" track.
Your definitions may not always enable to distinguish oligarchy from democracy, because the "entire electorate", without any other specification, may be an "inner circle". This, indeed, is about "how large is the selectorate?", and "democracy", here (when it comes to distinguish it from "oligarchy"), implies a pure democracy ("universal suffrage" coupled to a "direct democracy").
As no such pure democracy exists nor existed, our debate seems moot. In more than one way delegation, more precisely the "Consent of the governed" concept ( https://en.wikipedia.org/wiki/Consent_of_the_governed ), may be our central concept.
Moreover one may always argue that a pure democracy isn't sufficient to escape from oligarchy, because I can't see why 'Manufacturing Consent' ( https://en.wikipedia.org/wiki/Manufacturing_Consent ) wouldn't work.