My point is that appointments and elections are almost the same thing, nearly a distinction without a difference. Don't like the appointments, then vote for a different person. Bit of a distinction of representative democracy vs direct. Not necessarily that different. Almost entirely equally broken IMO.
> situation where one of the 10 people gets to pick the prosecutor!
That is not at all the simplification. We could change it that the 10 people are voting for someone to do the appointment of a prosecutor. Or we could flip it to a real world example where someone is in eastern oregon voting conservative, or someone lives in 1930s rural south as a minority.
The majority rule can lead to a bad path. Notably authoritarian regimes where the prosecutor promises to go after the minorities. Which has its examples historically throughout the world, including the US
All this other stuff about language is not relevant and I don't care about your thought experiment because it's completely unlike the way elections work in the real world, and has nothing to do with me preferring that over a situation where one of the 10 people gets to pick the prosecutor!