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.
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Best posts made by Matija
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Biproportional representation as a means to prevent bullet votingposted in Multi-winner
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RE: Good simple semi-PR methods?posted in Proportional Representation
@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.
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Alternative approval ballotsposted in Election Policy and Reform

If the candidates are grouped by party and voters can vote for those groups then ballots can be filled out faster. -
RE: Good simple semi-PR methods?posted in Proportional Representation
@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.