Algorithmic Approaches to Opinion Selection for Online Deliberation: A Comparative Study

In a deliberative poll, once submissions outnumber what anyone will read, some mechanism chooses which arguments each voter sees, acquiring much of the decision; practice delegates it to opaque learned rankers, so a voter cannot recompute or contest the exposure that shaped their vote. We ask whether it can be a published rule over publicly recomputable evidence with parameters held by the voter, treating legibility as an admissibility condition on usable mechanisms, not an objective traded against accuracy. We formalise a poll over bipolar justification sets, judging a slate by reason coverage, the order it arrives in, and captured endorsement mass; we give seven checkable criteria for a civic recommender and a rule meeting them: a one-hop reversed endorsement flow parameterised by a relation-weight function. An agentic simulator records every slate at every vote, over about 17,000 seed-paired runs. Served slates fall 0.035 short of a label-reading ceiling upper-bounding every selection procedure, opaque ones included: any unconstrained ranker's advantage is bounded and small. On coverage alone, with non-degenerate authoring, the rule is indistinguishable from a random slate, a null due to an order-blind, charity-blind instrument; on the other two it leads at every prefix by a margin widening with adversarial pressure and dominates on mass by a factor of 3.3. Once a realistic fraction of submissions carries no reasons, the coverage margin returns and grows. Label-homogeneous flooding collapses completeness from 0.81 to 0.34 under a flat weight policy, only to 0.44 under author-count normalisation, making the weight function a security control worth 10% of completeness. The choice between ranking arms is a position on a coverage-versus-mass frontier, not a fact, the kind of choice only a legible rule can hand to the person it affects. It maps onto an open-source peer-to-peer platform.

A primary goal of online deliberation platforms is to identify ideas that are broadly agreeable to a community of users through their expressed preferences. Yet, consensus elicitation should ideally extend beyond the specific statements provided by users and should incorporate the relative salience of particular topics. We address this issue by modelling consensus as an interval in a one-dimensional opinion space derived from potentially high-dimensional data via embedding and dimensionality reduction. We define an objective that maximizes expected agreement within a hypothesis interval where the expectation is over an underlying distribution of issues, implicitly taking into account their salience. We propose an efficient Empirical Risk Minimization (ERM) algorithm and establish PAC-learning guarantees. Our initial experiments demonstrate the performance of our algorithm and examine more efficient approaches to identifying optimal consensus regions. We find that through selectively querying users on an existing sample of statements, we can reduce the number of queries needed to a practical number.

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 $x_j$ within batches $X=(x_1,\dots,x_m)\in(\mathbb{R}^d)^m$, where each item's ranking is dictated by its score $\langle θ^*,x_j\rangle$ according to a fixed scoring vector $θ^*$. Given voters' preferred scoring vectors $θ^{(1)},\dots,θ^{(n)}$ and their population fractions $α^{(1)},\dots,α^{(n)}$, 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.