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.

@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.

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.

I think it's clear why this would not produce proportional outcomes: with voting taking place on two separate ballots, there would be no way to balance out independents' seats. Some political parties could even exploit this flaw. Such a system would be worse than the current party lists system.
There will be a referendum on whether we should adopt that electoral system.

@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.

A simple way to calculate sequential Ebert is to add for each already elected candidate, the number of voters who voted for both already elected candidate and considered candidate divided by number of voters who voted for already elected candidate. Then plug the sum into Sainte lague formula as number of party seats.

@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.

@isocratia said in Vertical composition of multiwinner approval methods:

My basic use-case for this technique is when the first phase is simple bloc approval voting that filters out anyone with more than, say, 75% disapproval (this threshold is a parameter), and the second phase is some proportional approval voting method.

I would do the opposite: filter out anyone who would skew proportionality then apply a single winner method.

In MMP, a district seat is typically assigned to the party which nominated the winner of that district. But what if instead we check which parties the winner's supporters voted for and then split the seat among those parties?
For example, if 50% of winner's supporters voted for party A, then that party would get half of the district seat.
As long as every district winner receives more than 50% of the vote this would prevent overhang seats.

One option would be 3s/2+4s+5s