Researchers propose proportional voting rules for negative ballots

Most committee election research assumes voters only approve candidates they like. This paper, posted on arXiv (2503.01985), extends proportionality to settings where voters can also vote against candidates—a common feature on platforms like Reddit or Doodle. The authors propose two distinct interpretations of negative votes. In the first, preventing disapproved candidates from winning carries equal weight to electing approved ones. In the second, approvals and disapprovals are treated as separate axes, each with its own fairness guarantees.

To evaluate these interpretations, the team introduces new axioms for proportional representation and analyzes whether they can be satisfied by three prominent voting rules: Phragmén's rule, Proportional Approval Voting (PAV), and the Method of Equal Shares (MES). They show which rule variants meet which axioms, offering a theoretical toolkit for designing fairer negative-vote systems. For practitioners, this means online polling and participatory budgeting platforms could eventually adopt rules that handle downvotes without sacrificing minority representation.