AI alignment and participatory design motivate a new democratic design problem: how to collectively choose a decision rule to use repeatedly. We study this problem for linear ranking rules, which repeatedly rank items
xj within batches
X=(x1,…,xm)∈(Rd)m, where each item's ranking is dictated by its score
⟨θ∗,xj⟩ according to a fixed scoring vector
θ∗. Given voters' preferred scoring vectors
θ(1),…,θ(n) and their population fractions
α(1),…,α(n), we ask how to choose a collective vector
θ∗ satisfying individual proportionality (IP): every voter type
i should agree with the resulting rankings to an
α(i)-proportional degree, either on average over time (long-run IP) or even within each batch (per-batch IP). The default rule, the arithmetic mean of the
θ(i), has been shown to be severely majoritarian; more generally, it is not clear that any fixed linear rule can balance many voters' disparate opinions. Our main result is that, surprisingly, there is a simple rule that does satisfy long-run IP: the angular mean, the spherical analog of the arithmetic mean. We then show that exact per-batch IP is impossible for fixed linear rules, but that the gap between per-batch and long-run IP shrinks quickly with batch size. Experiments on three real-world preference datasets show that all rules perform similarly when voters' preferences are homogeneous, while the angular mean substantially improves proportionality in high-disagreement regimes.