In no way this is a good example of such a system, but I still find Bosnia and Herzegovina political system absolutely hilarious. After Dayton peace agreement the literally put ethnicity requirement for presidents to Constitution as a hard rule. One Bosnian, one Serb and one Croatian. And yes, the country is ran by 3 presidents at the same time. So there is no longer a competition whether the main guy in the country will be theirs or ours.
There were two guys: a Roma and a Jew in BiH who also wanted to take the president office. However according to Constitution they didn't have a chance. So they went to EU Human Rights Court to look for a justice. The court told the country it's kinda racist to have a rule like that and they should change it. This was like 15 years ago. Guess whether the rule has changed since then. (Sejdić and Finci v. Bosnia and Herzegovina for more details).
PS. If you find 3 presidents not fascinating enough, then google for High Representative for Bosnia and Herzegovina.
There were two guys: a Roma and a Jew in BiH who also wanted to take the president office. However according to Constitution they didn't have a chance. So they went to EU Human Rights Court to look for a justice. The court told the country it's kinda racist to have a rule like that and they should change it. This was like 15 years ago. Guess whether the rule has changed since then. (Sejdić and Finci v. Bosnia and Herzegovina for more details).
PS. If you find 3 presidents not fascinating enough, then google for High Representative for Bosnia and Herzegovina.