From https://en.wikipedia.org/wiki/Oligarchy :
Especially during the fourth century BC, after the restoration of democracy from oligarchical coups, the Athenians used the drawing of lots for selecting government officers in order to counteract what the Athenians saw as a tendency toward oligarchy in government if a professional governing class were allowed to use their skills for their own benefit.[5][page needed] They drew lots from large groups of adult volunteers that pick selection technique for civil servants performing judicial, executive, and administrative functions (archai, boulē, and hēliastai).[6] They even used lots for posts, such as judges and jurors in the political courts (nomothetai), which had the power to overrule the Assembly.[7]
This sounds to me like an extreme thought experiment in democracy, it's hard to imagine it actually taking place! Any interesting stories about what happened as a result?
As your question asks about any interesting stories about what happened as a result, I think it is worth bringing up the comedy The Wasps by Aristophanes. In it a young Athenian tries to dissuade his elderly father from signing up to be a juror in the law courts. Volunteers, often older men, would volunteer at the courts and juries would be selected by lot, hear the day's cases, and receive a payment of three obols. The father in the story loves being a juror as he feels very powerful and is pandered to by lawyers and orators. On the other hand the son sees that the pandering and power is all a facade, and really these old men are the pawns of powerful demagogues. The play begins with the son and his slaves struggling to physically imprison the father in the house, and proceeds to a debate between the two. For a contemporary view of the pros and cons of office by lot, and simply for a very entertaining and genuinely funny play, it is well worth a read.