The article cites examples thereof, ranging from trade union leaders elected as supposedly fake “Slavic #Macedonians” in #Romania, #Bosniak & #Roma lists, redoubling the #Serb List in #Kosovo, and – needless to say – the #Komšić dilemma in #Bosnia-Herzegovina.

50 copies are for free: https://www.tandfonline.com/eprint/V7ABGDYNABHJKQQM7V8W/full?target=10.1080/13510347.2022.2157404

3. More generally, when more votes are needed for a seat A than for a seat B, then voters make their choice no longer on solely programmatic grounds, but rather need to balance their representative weights and their favourite policies.

This violates “vote neutrality”. This is a severe violation of the democratic principle. Does this problem emerge in any other democratic election? Maybe not surprisingly, in several of the cited cases, elections have resulted in crises of legitimacy. ...

With these inter-dependencies and electoral swings, the electoral accountability of representatives to their electorate is undermined.

2. Even more severe, imagine that the election of an A-seat is non-competitive, (e.g. because of a popular incumbent). Strategic A-voters might cast a vote for a B-candidate, who shares their preferences. In the end, both representatives A & B represent the same views. ...

„Usual“ quotas & second chambers in federal states often over-represent some voters. This is their purpose, so it's ok.
Quotas discussed here are more specific:they reserve seats for specific groups,but representatives are elected by all voters at large („liberal voting rights“).

Some (paradoxal) implications:

1. There are seats for group A and group B. Every voter can vote for either A or B. Hence, the competition for seats A will affect who is being elected for group B, and vice-versa. ...

@tonirodon

Tentatively, I would plea that we need to distinguish between the validity of a measure, and the validity of a point estimate, esp. of point estimates that appear surprising at first. (And probably, this would lead to a discussion about what type of variables should be displayed as maps, and which ones not.)

The authors are responsible for the variable (and the map). The emphasis on the point estimate is yours, and I wouldn't dare to make the authors responsible for it.

@tonirodon

Did you look up the construction of the measure for Catalonia (i.e. were all relevant dimensions of polarisation captured)?

"each party in the national ballot box"... were Catalan parties included?

If yes, what is the effect of weighting with the vote share? What happens if you calculate regional polarisation with reg. vote %?

If not so, there might be a substantial groups or respondents who dislike all (Spanish) parties to a similar degree, which seems to lead to a low score.