Approval voting was widely used in an experiment with introducing democracy in the Soviet Union started by M.S.Gorbachev. On 21 June 1987, elections were held in approximately 5% of all the USSR's 50,000 villages, towns, cities, and counties; making this by far the largest political approval voting elections ever conducted (up to the year 2000 anyhow). However, the experiment did not last long because the USSR collapsed a few years after they began it!
These were genuine elections (don't be misled by my word "experiment") and they were genuine approval-voting elections (not a variant form like in the early USA) although psychologically different because they expressed it as "disapproval" rather than "approval" voting.Theodore Shabad: Soviets to begin multicandidate election experiment in June, NY Times (15 April 1987) A6.
Bill Keller: In Southern Russia, a glimpse of democracy, NY Times (20 June 1987) A1 and A5.
Bill Keller: Gorbachev's Big Plan for Change: Is It Real or Just a Pipe Dream? New York Times 5 Dec 1988.
Bill Keller: Moscow says changes in voting usher in many local leaders, NY Times (21 Sept 1988) A1 and A7.
Bill Keller: 21 June A1+A11, and Bill Keller: THE ESTONIANS SAY, LET US BE ESTONIAN; Popular Front, With Unusual Vigor, Is Presenting Many Demands to Moscow, 2 Oct 1987 page 15. This is about how Estonia allowed "non communist front" to form (opposition party, 60K active members) and they were allowed to participate in the June 1987 AV elections. Again this regarded by top leaders as experiment in democratization.
Bill Keller: Armenians Astir: Write-In Candidate Wins 78%, NY Times 12 Oct 1988 page A3. A furor erupts when an unorthodox candidate wins.
Federal Election Commission: Report of visit by the FEC to the Soviet Union, June 1989 [Washington DC].