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.
Figures & tables
Figure 1: Motivation. One shared pantry yields different safe recommendations for members with different dietary rules, so household recommendation is an allocation problem rather than a ranking repeated for each member.
Figure 2: FairFRESH. Taste, retrieval-augmented dietary, and pantry encoders, fused by multi-head attention, produce a utility for every member–food pair. An allocation rule (utilitarian, max-min, or Nash) assigns foods from the utility matrix, a symbolic filter removes unsafe foods, and a post-hoc module turns Shapley and Banzhaf attributions into natural-language explanations without affecting any decision.
Method
Recall@20
NDCG@20
Popularity
0.235 [0.221, 0.248]
0.253 [0.241, 0.265]
Repeat-D1
0.321 [0.304, 0.339]
0.376 [0.358, 0.393]
BPRMF
0.220 [0.206, 0.234]
0.234 [0.220, 0.249]
NeuMF
0.111 [0.105, 0.117]
0.141 [0.133, 0.149]
LightGCN
0.244 [0.231, 0.258]
0.262 [0.250, 0.274]
GRU4Rec
0.207 [0.195, 0.220]
0.234 [0.220, 0.247]
Table 1: Individual-level accuracy on 400 test users (mean over five seeds for trained baselines; 95% user-bootstrap confidence intervals in brackets).
Strategy
Recall@20
Min Util.
Gini
NSW
A) Independent
0.266 [0.250, 0.282]
9.79 [9.36, 10.21]
0.109 [0.100, 0.118]
12.76 [12.42, 13.09]
B) Conflict resolution
0.180 [0.165, 0.194]
5.35 [5.00, 5.70]
0.192 [0.180, 0.205]
8.54 [8.25, 8.81]
C) Utilitarian
0.194 [0.180, 0.209]
7.64 [7.31, 7.96]
0.146 [0.136, 0.155]
10.72 [10.45, 10.99]
D) Max-Min
0.188 [0.173, 0.202]
8.75 [8.41, 9.08]
0.088 [0.079, 0.096]
10.56 [10.27, 10.87]
E) Nash
0.197 [0.182, 0.211]
8.56 [8.23, 8.89]
0.112 [0.103, 0.121]
10.98 [10.70, 11.27]
Table 2: Household allocation on 100 held-out four-person households, with 95% household-bootstrap confidence intervals. Higher is better except for Gini. Bold marks the best coordinated strategy (B–E) in each column; A is an uncoordinated reference that may give the same food to several members.
Figure 3: Scaling with household size, plotted from Table 6 . (a) Gini of per-member utility (lower is more equal). (b) Minimum member utility (higher is better). Percentages mark the changes from n=2 to n=6 discussed in the text. Independent recommendation (dashed) is an uncoordinated reference (Section 5.3 ).
Model
Recall@20
CSR
Gini
NSW
Full FairFRESH
0.197
1.000
0.112
10.98
w/o Pantry (availability) Encoder
0.064
1.000
0.160
5.58
w/o Medical Constraint
0.194
0.856
0.124
9.23
w/o Fairness Optimizer (utilitarian)
0.194
1.000
0.146
10.72
w/o RAG Constraint Encoder
0.200
1.000
0.087
10.06
Table 3: Component ablation on the held-out four-person households of Table 2 , under Nash allocation unless stated. The full model’s Recall@20 (0.197) lies below its individual-level value in Table 1 (0.293) because each food goes to one member. CSR is measured against the full rule set.
Figure 4: Game-theoretic explainability on 500 held-out households of two to six members. (a) Attribution faithfulness: correlation r between each component’s attribution and the utility drop observed when that component is removed. (b) Mean Shapley and Banzhaf attribution per component, sorted by Shapley value. Safety is not a player, since the filter is a hard constraint rather than a source of utility (Section 3.5 ).
Strategy
Mean Util.
Min Util.
Gini
Full Meal
Pantry Used
Indian recipes, simulated utilities
Unstructured
5.34
4.92
0.029
28.6%
4.59%
Structured individual
5.26
4.86
0.030
100%
5.12%
Structured shared
5.06
4.74
0.024
100%
3.47%
NHANES foods, learned utilities
Unstructured
5.58
5.10
0.029
0.6%
10.74%
Table 4: Shared versus individual meals on four-person households ( K=6 ; 100 households under each of five seeds). Values are means over seeds; standard deviations across seeds are at most 0.05 for utilities, 0.003 for Gini, 2.3 points for full meal, and 0.12 points for pantry used. Per-item utilities are min-max normalized. Higher is better except for Gini and pantry used. Bold marks the best value in each column within a setting.
Appendix figures & tables3 assets
Supplementary material from the paper’s appendix.
Appendix
n
Utilitarian: greedy/opt.
Max-min: greedy/opt.
Nash: Φϵ /upper bound
2
0.986 [0.982, 0.990]
0.978 [0.973, 0.983]
0.996 [0.995, 0.997]
3
0.975 [0.971, 0.980]
0.957 [0.950, 0.964]
0.990 [0.988, 0.992]
4
0.976 [0.972, 0.980]
0.946 [0.937, 0.955]
0.987 [0.985, 0.989]
Appendix
Table 5: Greedy allocation relative to exact optima (mean over 100 held-out households per size, with 95% bootstrap intervals).
n
Strategy
Recall@20
NDCG@20
PUR
Min Util.
Gini
NSW
Items
2
A) Independent
0.292
0.292
0.187
11.37
0.072
12.96
20.0
2
B) Conflict resolution
0.252
0.263
0.142
8.92
0.105
10.82
15.1
2
C) Utilitarian
0.264
0.270
0.184
10.34
0.086
12.16
20.0
2
D) Max-Min
0.260
0.268
0.185
10.84
0.061
12.13
20.0
2
E) Nash
0.267
0.273
0.185
10.75
0.072
12.30
20.0
3
A) Independent
0.283
0.291
0.279
10.36
0.096
12.87
20.0
Appendix
Table 6: Household allocation across household sizes n=2 – 6 (100 held-out households per size). CSR is 1.00 in every row. Items is the mean number of foods each member receives; strategies A and C–E always fill all K=20 slots. Bootstrap confidence intervals are released with the code.
Bacon, fried eggs, French dressing, tap water, toasted wheat bread, heavy cream
5.85
Bread 0.23, beans 0.17; bacon, fried eggs, French dressing, tap water
4.33
Complete meals: 0 of 4 (single-serving) vs. 4 of 4 (shared). Pantry used: 14.35% vs. 10.71%.
Appendix
Table 7: Worked example: one held-out NHANES household with learned utilities, K=6 . Single-serving allocation gives each member six foods; structured shared allocation cooks white bread and pinto beans once for all members and adds four individual foods. Totals are bundle utilities on the min-max-normalized scale. Both shared dishes are safe for every member.
Fair resource allocation studies how to distribute scarce goods, services, and computing capacity equitably while accounting for efficiency and constraints.
One of the many fairness definitions pursued in recent recommender system research targets mitigating demographic information encoded in model representations. Models optimized for this definition are typically evaluated on how well demographic attributes can be classified given model representations, with the (implicit) assumption that this measure accurately reflects recommendation parity, i.e., how similar recommendations given to different users are. We challenge this assumption by comparing the amount of demographic information encoded in representations with various measures of how the recommendations differ. We propose two new approaches for measuring how well demographic information can be classified given ranked recommendations. Our results from extensive testing of multiple models on one real and multiple synthetically generated datasets indicate that optimizing for fair representations positively affects recommendation parity, but also that evaluation at the representation level is not a good proxy for measuring this effect when comparing models. We also provide extensive insight into how recommendation-level fairness metrics behave for various models by evaluating their performances on numerous generated datasets with different properties.
Bjørnar Vassøy, Benjamin Kille, Helge Langseth
Norwegian University of Science and Technology, Trondheim, Norway
When an AI algorithm makes decisions that affect more than one person, aligning it becomes a problem of social choice: how should people's divergent preferences about system behavior be reconciled and aggregated into a single coherent model? The standard approach to aligning frontier AI models\unicodex2013reinforcement learning from human feedback\unicodex2013largely sidesteps this question and has poor social choice guarantees. However, it remains unclear what alternative should replace it. We show that, by focusing directly on an algorithm's welfare consequences, the alignment problem can be reformulated as linear optimization over a convex impact space, which makes it amenable to the standard toolkit of welfare economics and mechanism design. This reformulation clarifies how alignment protocols translate into welfare consequences and, conversely, how a social planner's desired constraints on welfare consequences can be translated back into alignment protocols. We apply this transformation to show that voting-by-issues and random-dictatorship mechanisms are strategyproof and unanimous. Demonstrating the reverse direction, we also apply the impact representation to derive a family of alignment protocols that maximize utilitarian social welfare subject to various social desiderata, such as bounds on individual or group harm. We illustrate the welfare implications of these alignment protocols empirically using real human preferences over kidney allocation, charitable food distribution, LLM responses, and trolley problems.
Zachary Wojtowicz, Michelle Si, Finale Doshi-Velez +1
MIT Cambridge, MA 02139 · Harvard University Cambridge, MA 02138
Fair allocation of scarce, indivisible resources is an important challenge in many societal problems. While there are several formal theories of fairness, no single definition can always be satisfied. As large language models (LLMs) are increasingly used to support decisions and act as agents, they raise new concerns about distributional justice: their judgments are not directly tied to any specific fairness framework and may violate key normative principles. In this work, we introduce a general method for evaluating fairness reasoning in LLMs. We study first-person fairness judgments across a broad set of models and compare them directly with human responses on matched scenarios and elicitation conditions. We find that LLMs tend to prefer stricter fairness constraints than humans, show more self-interested behavior, are sensitive to how information is framed, and are difficult to align with human judgments using fine-tuning with current datasets.
Qishen Han, Hadi Hosseini, Joshua Kavner +3
Rutgers University · Pennsylvania State University · Independent Researcher +1