Hodge-Guided Active Preference Elicitation for Efficient Pairwise Ranking
Eskander Bejaoui, Mohamed Ould-Elhassen Aoueileyine, Ridha Bouallègue · International Journal of Advanced Computer Science and Applications · 2026
Pairwise comparison is a standard method for eliciting user preferences in recommender systems and group decision-making. The number of required comparisons grows quadratically with the number of alternatives, creating a substantial burden for users and platforms. This paper asks whether Hodge decomposition, which splits a preference flow into gradient (consensus), curl (local inconsistency), and harmonic (global inconsistency) components, can guide which comparisons to request, rather than merely aggregate whichever comparisons arrive. Preference elicitation is formalized as a sequential acquisition problem for online HodgeRank. Seven acquisition policies are evaluated, including two novel Hodge-informed policies: HarmonicReduce, which targets edges likely to carry harmonic inconsistency, and FlowClone, a lightweight neural policy trained by behavioural cloning on a compact five-dimensional feature representation. A Bayesian Bradley-Terry active-learning baseline (BALD) is also included. Policies are evaluated on three real-world datasets under a leakage-free protocol: held-out relevance labels come from full-data batch HodgeRank, tracked via normalized discounted cumulative gain, and validated under five-fold leave-users-out cross-validation so every user is evaluated once. Across all three datasets, geometry-informed active policies cut the comparisons needed to reach a fixed recommendation-quality threshold by roughly half relative to random sampling (43–56% depending on dataset). They consistently outperform BALD, which is itself a statistically confirmed improvement over random sampling on two of the three datasets. This advantage depends on the scoring model: pairing active acquisition with a Borda count aggregator produces worse outcomes than random acquisition with HodgeRank, a phenomenon termed the Borda collapse and confirmed significant, in both directions, by paired Wilcoxon tests with Holm-Bonferroni correction. HarmonicReduce’s effectiveness depends on comparison-graph density, a pattern proven exactly from the circuit rank of the comparison graph. These findings show that Hodge-theoretic structure is informative not only for aggregating collected preferences, but also for deciding which preferences to collect.