This assumes that elections are necessary for democracy. However this is wrong and the ancient greek already knew that: "It is democratic for state offices to

This assumes that elections are necessary for democracy. However this is wrong and the ancient greek already knew that: "It is democratic for state offices to be filled by lot, and oligarchic for them to be filled by election" (Aristotle, Politics) This idea was the majority view until the French revolution: "The decision by lot corresponds to the nature of democracy, the decision by election to that of aristocracy." (Montesquieu, The Spirit of Law) So, just because voting systems cannot be perfect doesn't mean democracy is mathematically impossible. In fact mathematically and statistically democracy is only possible without any elections, simply by choosing candidates by lot, see https://en.wikipedia.org/wiki/Sortition https://en.wikipedia.org/wiki/Sortition .