The country of Equestria in My Little Pony: Friendship is Magic seems to be a dual monarchy (or, if you want to be strict with language, a principality) ruled by Princesses Celestia and Luna (with a period of sole rule by Celestia during Luna's exile).
Does Equestria have meaningful elections of any kind at any level (e.g. a legislative assembly, citizens' advisory council, etc.)? The town of Ponyville seems to have a Mayor, which, in English speaking countries, is typically an elected office, and she acts more like a politician than an aristocrat, but I don't recall any specific mention of anyone who either did or did not vote for her (so it's not clear if she was elected by the citizens, was appointed by Celestia, or inherited her office).