I got an impression that in proportional approval voting, at least some voters might be incentivized to bullet vote for candidates who live nearby. Some level of biproportionality may remove this incentive.

https://en.wikipedia.org/wiki/1925_German_presidential_election

@anniek Sequential Ebert is precinct summable and fully proportional. It still has rounds but doesn't require counting ballots more than once. Might be what you're looking for.

@toby-pereira It's simpler to count and simpler to compute. ABC+A+B+C might be slightly more monotonic and is equivalent to using d'hondt formula.

@toby-pereira I'm copying the non-awardment version of MMP, which is more proportional than others.

@toby-pereira The first step is to guarantee every district a locally supported MP as long as they can agree on who should represent them.

Election takes place in a district cluster comprising 10 or more districts, each to be represented by 2 MPs. Each candidate runs in a single district but voters can vote for any candidates in the cluster.
In each district the candidate that got the largest number of votes from their own district is elected as long as that number is not smaller than Hare quota.
Candidates are elected step by step until each district has two MPs representing it. In each step the candidate with the most favorable ABC+A+B+C score among the candidates with less than 2 MPs already representing their district is elected.

@toby-pereira the problem I see with approval is that political parties could split to get more funding.

https://en.wikipedia.org/wiki/1925_German_presidential_election

Two-round presidential election with 3 candidates in the second round is a factor I can think of.

With ranked voting it's easy - just take the top choice of every voter and use that for the amount of funding each candidates' party receives for the next election.

The governing coalition opted for open lists. Phragmén-MMP would be better because we generally like the idea of independent candidates.
Though open lists are still better than MMP with runoff.

@lime I was talking about bullet voting with the goal of gaining a representative who lives nearby.

I got an impression that in proportional approval voting, at least some voters might be incentivized to bullet vote for candidates who live nearby. Some level of biproportionality may remove this incentive.