Proportional Decision Rules for Repeated Ranking

A new arXiv paper studies how to collectively choose a linear ranking rule for repeated decisions, aiming for proportional representation of voter preferences. The problem involves ranking items within batches based on scores from a fixed scoring vector. Given voters' preferred scoring vectors and their population fractions, the goal is to select a collective vector that satisfies individual proportionality (IP), meaning each voter type agrees with the resulting rankings to a degree proportional to their population share. The paper distinguishes between long-run IP (average over time) and per-batch IP (within each batch). It notes that the arithmetic mean of voters' vectors is severely majoritarian, motivating the search for better rules. The work is motivated by AI alignment and participatory design, addressing democratic decision-making in algorithmic contexts.