FairFRESH: A Neuro-Symbolic Framework for Fair and Explainable Household Food Recommendation
Abstract: Recommender systems typically serve one user at a time. However, in households, members share a finite pantry and follow different dietary rules, making independent recommendations prone to resource conflicts and dietary violations. We formulate household food recommendation as constrained fair division and present FairFRESH, a neuro-symbolic framework that learns per-member utilities, allocates foods under explicit welfare objectives, enforces dietary rules through a deterministic filter, and explains recommendations using Shapley and Banzhaf attributions. Theoretically, we show that no finite penalty guarantees compliance near a dietary-rule threshold, establish approximation guarantees for greedy allocation under utilitarian and smoothed Nash objectives in the stock-free model before filtering, and characterize the scale invariance of Nash welfare. We also use the minimax theorem to analyze rotating shared meals. On NHANES-derived data, the learned utility model achieves Recall@20 of 0.293, outperforming five learned recommenders (at most 0.244) but not a previous-day repetition heuristic (0.321). On held-out four-person households, Nash allocation reduces Gini disparity by 42% relative to conflict resolution while improving Recall@20 from 0.180 to 0.197. It comes within 2% of an upper bound on the smoothed Nash optimum, and rescaling one member's utilities changes at most 1.5% of assignments. All recommendations satisfy the encoded dietary rules, while attribution scores correlate with utility loss upon component removal (r = 0.76). In simulation, shared meals reduce pantry use by about one-third, and weekly rotation increases the worst-off member's utility by 38% over the best fixed meal.