In the previous planting asking whether free-list PR violated my own definition of a “simple system, I mentioned the criterion of avoiding violation of the rank-size principle in allocation of seats to votes within district (see footnote 2). I later happened up a major example of violation of the rank-size principle: Kosovo in 2021!
It is a single district of 120 seats, but per Wikipedia:
The Assembly had [under the Constitutional Framework] 120 members elected for a three-year term: 100 members elected by proportional representation, and 20 members representing national minorities (10 Serbian, 4 Roma, Ashkali and Egyptian, 3 Bosniak, 2 Turkish and 1 Gorani). Under the new Constitution of 2008, the guaranteed seats for Serbs and other minorities remains the same, but in addition they may gain extra seats according to their share of the vote.
The result of this is that there are parties with as much as 2.5% of the votes but no seats (there is also a 5% legal threshold for non-ethnic parties), and parties with as little as 0.14% who have seats when somewhat larger ethnic parties do not. For instance, the United Roma Party of Kosovo has a seat with 1,208 votes while the Innovative Turkish Party, which I presume is an “ethnic” party, with 1,243 votes, has none. That would be because the two set-aside Turkish seats were won by the Turkish Democratic Party of Kosovo, which had almost 6,500 votes (0.75%).
Perhaps it is not a “single district” and we should think of each ethnic group’s set-aside representation as a distinct district in addition to the general constituency. But that is certainly not how I generally understand “district.” In any case, there is nothing “simple” about the provision or its impact on outcomes, particularly regarding the rank-size criterion.
In addition, these provisions result in the odd case of a party with a majority of the vote not getting a majority of the seats, which is certainly unusual for a proportional representation system!