The pope, who is the absolute monarch of the state of the Holy See, is elected by vote of the (presumably) non-citizen cardinals. I can’t think of any other nations where the electorate is composed even partially, never mind almost entirely, of non-citizens.
Am I just unable to come up with any? Or is this a great bar trivia question?
Cardinals are “Princes of the Church” and have dual citizenship with the Vatican and their homelands.
Andorra, a tiny nation in the Pyranees, is governed jointly by two Princes: The President of France and the Bishop of Urgel in Spain). Andorrans don’t select either of these men.
The UK allows Irish and Commonwealth citizens to vote in general elections (obviously the Prime Minister isn’t directly elected, but I suppose it’s the same deal).
When I lived in New Zealand, even though I was a U.S. citizen I was not just allowed, I was required (like all residents of the country, I believe) to vote in the parliamentary elections. (In 1984 I voted in both the U.S. presidential election by absentee ballot, and in the N.Z. parliamentary elections).
Many American states also granted voting rights to non-citizens at one time. A few cities still do so (for municipal elections) today. We had a recent thread on this; I’m too lazy to look it up right now, but until about 1900 something like 19 states allowed non-citizens to vote in both state and federal elections.