Paper deep dive
Aggregating User Preferences while Ensuring Equity, Diversity, and Inclusion using Graph Summarization
Adji Marieme Sita Cissé, Malek Mouhoub
Intelligence
Status: succeeded | Model: Gemma-4-26B-A4B | Prompt: intel-v1 | Confidence: 94%
Last extracted: 10/7/2026, 8:46:34 AM
Summary
The paper introduces AURORA, a graph summarization method for aggregating user preferences that explicitly enforces Equity, Diversity, and Inclusion (EDI) constraints. Unlike classical voting rules (Borda, Condorcet) or post-hoc fairness corrections, AURORA uses a greedy coarsening algorithm on weighted attributed bipartite graphs to merge user nodes while bounding degradation in equity gap, intra-list diversity, and group inclusion. Evaluated across five datasets (MovieLens, libimseti.cz, Rate My Professors, OpenAlex), AURORA demonstrates superior diversity gains and robust fairness-diversity trade-offs compared to baselines.
Entities (13)
Relation Signals (12)
Adji Marieme Sita Cissé → authored → AURORA
confidence 98% · Adji Marieme Sita Cissé... AURORA (Attributed Unified gRaph cOarsening for equitable RecommendAtion)
Malek Mouhoub → authored → AURORA
confidence 98% · Malek Mouhoub... AURORA (Attributed Unified gRaph cOarsening for equitable RecommendAtion)
AURORA → evaluatedon → OpenAlex
confidence 95% · We evaluate across five datasets... OpenAlex... AURORA... achieves the lowest equity gap... on OpenAlex
AURORA → evaluatedon → MovieLens-100K
confidence 95% · We evaluate across five datasets... MovieLens 100k... Our method, AURORA... on MovieLens 100k
AURORA → evaluatedon → Rate My Professors
confidence 95% · We evaluate across five datasets... Rate My Professors... On Rate My Professors, it combines high diversity
AURORA → evaluatedon → libimseti.cz
confidence 95% · We evaluate across five datasets... libimseti.cz... On libimseti.cz... our method... does not reduce the equity gap
AURORA → uses → Graph Summarization
confidence 95% · We address this problem through EDI-constrained graph summarization... Our method, AURORA... aggregates preferences through graph summarization under EDI constraints
AURORA → enforces →
Cypher Suggestions (0)
No Cypher suggestions yet.
Abstract
Abstract:Aggregating the preferences of diverse user groups into a collective outcome raises fundamental challenges of equity, diversity, and inclusion (EDI): classical aggregation rules such as Borda and Condorcet have no mechanism to prevent results from systematically favoring majority groups, collapsing onto homogeneous items, or under-representing minorities. We address this problem through EDI-constrained graph summarization. User preferences are modeled as a weighted attributed bipartite graph, and a greedy coarsening algorithm iteratively merges user nodes while enforcing three structural EDI criteria: an equity gap constraint ($\Delta E$), an intra-list diversity constraint (ILD), and a group inclusion constraint. Rather than correcting fairness after aggregation, our method embeds EDI preservation directly into the graph structure. We evaluate across five datasets spanning four domains: MovieLens 100k and 1M, this http URL, Rate My Professors, and OpenAlex (2018-2023). Our method, AURORA, achieves the largest and most consistent diversity gains over classical voting rules, and on MovieLens 100k at $k = 20$ it simultaneously improves all three EDI criteria over both Borda and Condorcet. On Rate My Professors, it combines high diversity (ILD = 0.808) with the highest female item representation (60%), at a moderate equity cost, and it achieves the lowest equity gap ($\Delta E = 0.031$) on OpenAlex, where Borda-based methods recommend zero female authors. On this http URL, the only dataset where the sensitive attribute is present on both sides of the bipartite graph, our method does not reduce the equity gap, a limitation we connect to prior findings that demographic parity is not always an appropriate target. These results demonstrate that embedding EDI constraints into aggregation structure yields more robust fairness-diversity trade-offs than post-hoc approaches.
Tags
Links
- Source: https://arxiv.org/abs/2610.07128v1
- Canonical: https://arxiv.org/abs/2610.07128v1
Trouble viewing inline? Open PDF directly →
Full Text
57,227 characters extracted from source content.
Expand or collapse full text
Aggregating User Preferences while Ensuring Equity, Diversity, and Inclusion using Graph SummarizationThanks: An interactive dashboard with the full experimental results is available at https://sitaacisse-boop.github.io/EDI/. Adji Marieme Sita Cissé Affiliation: Université Paris-Saclay, UVSQ, France Affiliation: Department of Computer Science, University of Regina, Regina, SK, Canada E-mail louzsita29@gmail.com, Malek.mouhoub@uregina.ca Malek Mouhoub Affiliation: Department of Computer Science, University of Regina, Regina, SK, Canada E-mail louzsita29@gmail.com, Malek.mouhoub@uregina.ca Abstract Aggregating the preferences of diverse user groups into a collective outcome raises fundamental challenges of equity, diversity, and inclusion (EDI): classical aggregation rules such as Borda and Condorcet have no mechanism to prevent results from systematically favoring majority groups, collapsing onto homogeneous items, or under-representing minorities. These tensions surface concretely in group recommendation, where optimizing for utility alone entrenches majority bias and filter bubbles. We address this problem through EDI-constrained graph summarization. User preferences are modeled as a weighted attributed bipartite graph, and a greedy coarsening algorithm iteratively merges user nodes while enforcing three structural EDI criteria: an equity gap constraint (ΔE E), an intra-list diversity constraint (ILD), and a group inclusion constraint. Rather than correcting fairness after aggregation, our method embeds EDI preservation directly into the graph structure. We evaluate across five datasets spanning four domains — movie recommendation (MovieLens 100k and 1M), social dating (libimseti.cz), educational rating (Rate My Professors), and academic authorship in AI/ML/CS (OpenAlex, 2018–2023). No single baseline simultaneously satisfies all three EDI criteria across domains. Our method, AURORA, achieves the largest and most consistent diversity gains over classical voting rules (Borda, Weighted Borda, Condorcet), and on MovieLens 100k at k=20k=20 it simultaneously improves all three EDI criteria over both Borda and Condorcet. On item-side equity settings, it uniquely combines high diversity (ILD == 0.808) with the highest female item representation (fracF=60%frac_F=60\%) on Rate My Professors — though at a moderate equity cost relative to Borda on this dataset — and achieves the lowest equity gap (ΔE=0.031 E=0.031) on OpenAlex, where Borda-based methods recommend zero female authors. On libimseti.cz, the only dataset where the sensitive attribute is present on both sides of the bipartite graph, our method — like classical voting rules — does not reduce the equity gap, a limitation we analyze and connect to prior findings that demographic parity is not always an appropriate target when preferences genuinely differ across groups. These results demonstrate that embedding EDI constraints into aggregation structure yields more robust fairness–diversity trade-offs than post-hoc approaches, while also revealing that no single compression budget or structural mechanism resolves the equity–diversity tension uniformly across domains. Keywords: graph coarsening · recommender systems · fairness · EDI metrics · preference aggregation · bipartite graph · social choice 1 Introduction As algorithmic systems increasingly mediate access to information, opportunities, and resources, ensuring that their outcomes do not systematically disadvantage certain groups has become a central concern across many domains, from hiring and lending to content curation [9]. Equity, diversity, and inclusion (EDI) capture three complementary facets of this concern: equity asks that outcomes not systematically favor one group over another, diversity asks that outcomes not collapse onto a narrow set of options, and inclusion asks that minority groups be adequately represented in the outcome. Recommender systems are a paradigmatic case in which these tensions surface concretely. They have become essential tools for navigating the vast amount of content available online, from movies to products to services, and their traditional goal is to maximize utility — that is, to predict as accurately as possible the items a user will like. However, optimizing for utility alone has well-documented drawbacks. It tends to reinforce the so-called Matthew effect, in which already-popular items are recommended ever more often, and it can trap users in filter bubbles of homogeneous content. These effects raise EDI concerns: collective recommendations may systematically favor the tastes of majority groups, offer little variety, and under-represent minorities. Addressing EDI in recommendation requires aggregating the preferences of many users into a collective outcome while treating user groups fairly. Existing approaches typically enforce fairness by modifying the input preferences [5], by modifying the output ranking through re-ranking [13], or by regularizing the learning algorithm [15]. In parallel, graph summarization offers a powerful way to reduce large user–item preference graphs into compact, tractable representations, but it has traditionally been guided by structural fidelity, storage, or query efficiency, never by the preservation of fairness. To the best of our knowledge, no existing work makes the preservation of equity, diversity, and inclusion an explicit criterion when summarizing a preference graph [8]. In this paper, we address this gap. We represent user preferences as a weighted attributed bipartite graph and propose AURORA (Attributed Unified gRaph cOarsening for equitable RecommendAtion), an approach that aggregates preferences through graph summarization under EDI constraints: instead of merging nodes solely to minimize structural error, we constrain the summarization so as to bound the degradation of equity, diversity, and inclusion. Our main objective is to construct a summary that reduces the size of the preference graph while preserving these three properties, and to compare it against five classical aggregation rules: Average Score, Borda, Weighted Borda, Condorcet, and Fair Re-rank. We instantiate and evaluate our approach across five datasets spanning four domains — movie recommendation (MovieLens 100k [4] and 1M), social dating (libimseti.cz), educational rating (Rate My Professors), and academic authorship in AI/ML/CS (OpenAlex, 2018–2023) — using gender as the sensitive attribute in all cases, applied either to users (user-side equity) or to recommended items (item-side equity). The remainder of this paper is organized as follows. Section 2 introduces the necessary background. Section 3 reviews related work. Section 4 presents our proposed methodology. Section 5 reports the experimental evaluation, and Section 6 concludes. 2 Background This section introduces the concepts and notation used throughout the paper: the preference graph, preference aggregation, graph summarization, and the notions of equity, diversity, and inclusion. 2.1 Preference Graph We represent preference data as a weighted attributed bipartite graph G=(U∪I,E,w,s),G=(U∪ I,\;E,\;w,\;s), where U=u1,…,umU=\u_1,…,u_m\ is the set of user nodes, I=i1,…,inI=\i_1,…,i_n\ is the set of item nodes (e.g. movies, professors, or researchers), and E⊆U×IE U× I is the set of edges. An edge (u,i)∈E(u,i)∈ E exists if and only if user u has rated item i. The weight function w:E→[1,5]w:E→[1,5] gives the rating assigned by u to i. The sensitive attribute s is defined on user nodes in user-side equity settings (s:U→F,Ms:U→\F,M\, e.g. MovieLens, libimseti) or on item nodes in item-side equity settings (s:I→F,Ms:I→\F,M\, e.g. Rate My Professors, OpenAlex), where F,M\F,M\ denotes the two gender groups. The graph is bipartite: edges connect only users to items, never two users or two items. 2.2 Preference Aggregation Preference aggregation is the task of combining the individual preferences of many users into a single collective outcome, typically a ranking or a top-k set of items [10]. Classical aggregation rules provide our baselines. The average score ranks items by their mean rating; the Borda count converts each user’s ratings into ranks and sums them; Weighted Borda normalizes Borda scores by group size to compensate for demographic imbalances; and the Condorcet method compares items pairwise, an item winning if a majority of users prefer it. None of these rules explicitly controls EDI during aggregation, which motivates the approach proposed in this paper. 2.3 Graph Summarization Graph summarization reduces a large graph to a smaller one that preserves selected properties of the original. We focus on the grouping (or aggregation) family in which nodes are merged into supernodes according to their similarity and the edges between groups are aggregated into superedges [8]. The process of merging nodes to obtain a smaller graph is called coarsening. The resulting summary is smaller and faster to process, but the merging necessarily discards information; the central question is therefore which properties the summary should preserve. 2.4 Equity, Diversity, and Inclusion We consider three distinct notions, jointly referred to as EDI. Equity refers to the fair treatment of groups defined by the sensitive attribute, so that no group is systematically favored or disadvantaged by the collective outcome — whether the group is defined on users (user-side equity) or on recommended items (item-side equity). Diversity refers to the variety of the recommended items, avoiding lists dominated by a single type or by the most popular items. Inclusion refers to ensuring that minority groups are represented in the outcome at least in proportion to their size. These three notions are distinct and can be in tension: improving one may degrade another. Our work treats them as properties to be preserved when summarizing the preference graph, and the precise metrics used to quantify them are defined in Section 4. 3 Literature Review Our work sits at the intersection of four research areas: preference aggregation and social choice, graph summarization, algorithmic fairness (equity, diversity and inclusion), and fairness-aware recommender systems. We review each in turn, and then identify the gap that our contribution addresses. 3.1 Preference Aggregation and Social Choice Preference aggregation, the problem of combining the individual preferences of many users into a single collective outcome, is the theoretical foundation of our work and is studied within computational social choice theory. Roy et al. [11] structure the problem along three dimensions, input format, output format, and aggregation rule, and survey how fairness has been addressed across classical voting rules such as Borda, Copeland, and single transferable vote. A central result framing the field is Arrow’s impossibility theorem, which shows that no aggregation rule can simultaneously satisfy a small set of reasonable fairness criteria; this motivates reasoning in terms of preserved properties rather than a single optimal rule. Notably, Roy et al. [11] distinguish between making an outcome fair by modifying the input preferences and by modifying the output ranking, an opposition we return to when positioning our own approach. Building on this tradition, Kellerhals and Peters [6] connect proportional clustering to multiwinner voting and show that three fairness notions, proportional fairness, individual fairness, and the transferable core, are closely related and can be satisfied simultaneously. Crucially for our setting, their analysis operates on a graph metric, grouping nodes into fair clusters, which is conceptually close to summarizing a preference graph while preserving fairness guarantees. 3.2 Graph Summarization Graph summarization aims to condense a large graph into a smaller representation that preserves selected properties of the original, thereby reducing storage, accelerating computation, and improving interpretability. Liu et al. [8] provide a reference survey of the field and organize existing methods into four families: grouping (aggregating nodes into supernodes based on structural or attribute similarity), bit compression, simplification or sparsification (removing less important nodes or edges), and influence-based approaches. A central observation of their survey is that there is no single definition of a good summary: the quality of a summary depends on the objective it is meant to serve. They further distinguish between plain, labeled (attributed), and dynamic graphs, a distinction directly relevant to our setting, since our preference graph carries a sensitive attribute on user nodes and is therefore a labeled graph. More recent work, surveyed by Shabani et al. [12], applies graph neural networks to summarization and classifies approaches into aggregation, selection, and transformation. Notably, this survey identifies task-based summarization, producing summaries tailored to a specific downstream need rather than generic ones, as an open research direction, and highlights the difficulty of defining quality metrics that depend on the target application. Our work belongs to the grouping/aggregation family and directly addresses this open direction: we propose a summary whose quality criterion is the preservation of equity, diversity, and inclusion. 3.3 EDI in Recommender Systems and Algorithmic Fairness The fairness, diversity, and inclusion (EDI) dimension is central to our work, and each notion has its own formalizations. Yao and Huang [14] study fairness in collaborative filtering and show that demographic parity is often inappropriate for recommendation, since user preferences genuinely depend on sensitive attributes such as gender; instead, they propose four unfairness metrics (value, absolute, underestimation, and overestimation unfairness), evaluated on MovieLens. We adopt their value unfairness as the basis for our equity metric. Leonhardt et al. [7] focus on user-side fairness and provide empirical evidence of a direct trade-off between diversity and user fairness: increasing aggregate diversity substantially increases disparity among users, as measured by two Gini-based metrics. This confirms that EDI objectives are in tension and must be balanced rather than jointly maximized. Zhao et al. [15] survey fairness and diversity in recommender systems, treat them jointly rather than in isolation, and classify mitigation techniques into pre-processing, in-processing, and post-processing; they also frame the problem as multi-objective optimization over a Pareto frontier of accuracy, fairness, and diversity. Finally, Dong et al. [3] survey fairness specifically in graph mining, the closest area to AURORA. They highlight that graphs raise fairness challenges absent from i.i.d. data, notably structural bias arising from homophily, and classify fairness notions (group, individual, counterfactual, degree-related, and application-specific) as well as mitigation techniques. Among the latter, edge rewiring is the only one that acts on graph structure, as AURORA does; however, it modifies the original graph by adding or removing edges, whereas we reduce the graph by merging nodes. Our equity metric corresponds to group fairness in their taxonomy. 3.4 Social Choice for Fairness-Aware Recommendation The work closest to AURORA in spirit combines social choice and fairness directly within recommendation. Aird et al. [1] introduce SCRUF-D, an architecture in which each fairness concern is modeled as an independent agent that expresses preferences over items; these agents vote alongside the base recommender, through voting rules such as Borda, Copeland, and Ranked Pairs, to produce the final ranking. A follow-up study [2] extends this framework to heterogeneous fairness, handling several fairness notions that differ in logic and measurement within a single system, including group proportional fairness, and evaluates it on MovieLens. Both works confirm a recurring finding: fairness and accuracy are in tension, and different aggregation rules trade them off differently. This line of work is our most direct conceptual competitor, yet it differs from AURORA in a fundamental way: SCRUF-D acts at the moment of producing the final ranking, that is, as a post-processing or re-ranking step, whereas we act upstream on the structure of the summarized graph. Their thorough exploration of the post-processing route leaves the structural route open. We do not implement it as an experimental baseline: SCRUF-D requires a per-fairness-concern utility function and an inter-agent negotiation mechanism (Borda, Copeland, or Ranked Pairs voting among agents) that would need to be designed and calibrated separately for each of our four corpora — a methodological contribution in its own right, distinct from our fixed-EDI-metric evaluation protocol. Fair Re-rank, our post-processing baseline, remains comparable in spirit (adjusting the final ranking under a fairness constraint) without requiring this multi-agent architecture; a faithful SCRUF-D implementation is left as a priority baseline for future work. 3.5 Research Gap Across these four areas, a consistent picture emerges. Fairness in recommendation has been addressed mainly through input or output modification, through pre-, in-, or post-processing, or through edge rewiring on the graph structure; graph summarization, in turn, has traditionally optimized structural fidelity, storage, query speed, or denoising. To the best of our knowledge, no existing work makes the preservation of equity, diversity, and inclusion an explicit quality criterion of a graph summary. This is precisely the gap our work addresses. We therefore study the following research question: given a weighted bipartite preference graph, how can we construct a summary, through community detection and coarsening, that reduces its size while bounding the degradation of equity, diversity, and inclusion, compared to classical aggregation rules? 4 Proposed Methodology Building on the graph model and background introduced in Section 2, this section defines the three EDI metrics precisely, formulates the constrained summarization objective, and describes how we derive a collective ranking from the summarized graph. 4.1 EDI Metrics Let R=(r1,…,rk)R=(r_1,…,r_k) denote a collective top-k ranking produced from the preference graph, and let F,M⊂UG_F,G_M⊂ U be the two user groups induced by the sensitive attribute s. Equity. We measure equity through the value unfairness metric of Yao and Huang [14]. For each group g∈F,Mg∈\F,M\, the group utility over the top-k list is utilityg(R)=1|g|∑u∈g1k∑i∈Rw(u,i),utility_g(R)= 1|G_g| _u _g 1k _i∈ Rw(u,i), (1) where w(u,i)=0w(u,i)=0 when (u,i)∉E(u,i)∉ E. The equity gap is then ΔE(R)=|utilityF(R)−utilityM(R)|. E(R)= |utility_F(R)-utility_M(R) |. (2) A value of ΔE E close to zero indicates that both groups derive similar average satisfaction from the collective outcome. Diversity. We measure diversity through the intra-list diversity (ILD) metric: ILD(R)=2k(k−1)∑i,j∈Ri≠jdist(i,j),ILD(R)= 2k(k-1) _ subarrayci,j∈ R\\ i≠ j subarraydist(i,j), (3) where dist(i,j)=1−cosine(i,j)dist(i,j)=1-cosine(v_i,v_j) and i∈ℝmv_i ^m is the rating vector of item i across all users, with i[u]=w(u,i)v_i[u]=w(u,i) if (u,i)∈E(u,i)∈ E and 00 otherwise. A higher ILD indicates a more varied recommendation list. Inclusion. We measure inclusion through a proportional fairness criterion grounded in the core concept of Kellerhals and Peters [6] and operationalized as the group proportional fairness metric of Aird et al. [2]. Let θ be a relevance threshold and αg=|g|/|U| _g=|G_g|/|U| the population share of group g. The inclusion score of group g is inclusiong(R)=1|g|∑u∈g|i∈R:w(u,i)≥θ|k.inclusion_g(R)= 1|G_g| _u _g |\i∈ R:w(u,i)≥θ\|k. (4) Inclusion is satisfied for group g when inclusiong(R)≥αginclusion_g(R)≥ _g: a group representing αg _g of the user population should find at least the same proportion of top-k items relevant. We set θ=4.0θ=4.0 as our default on the 1–5 scale and compare with θ=3.5θ=3.5, the threshold used by Aird et al. [2] to define a “liked” item on MovieLens (rating >3>3); this threshold is recalibrated per dataset to preserve the same semantics across different rating scales (see Section 5). Item-side equity. In item-side equity settings (Rate My Professors, OpenAlex), the sensitive attribute is defined on items rather than users. The primary inclusion metric is then the fraction of female items in the top-k list: fracF(R)=|i∈R:s(i)=F|k.frac_F(R)= |\i∈ R:s(i)=F\|k. The equity gap ΔE E is adapted accordingly, comparing the average utility received by female and male items across all users in the graph. 4.2 EDI-Constrained Graph Summarization Rather than enforcing EDI as a post-hoc correction on an already-computed ranking, our approach embeds EDI preservation directly into the coarsening process. Each candidate merge of user nodes is accepted only if the resulting summarized graph maintains the equity gap, intra-list diversity, and group inclusion of the original graph within prescribed tolerances. This structural integration ensures that fairness is not traded off against compression after the fact, but is preserved as the graph is progressively reduced. Coarsening. Starting from G=(U∪I,E,w,s)G=(U∪ I,E,w,s), we iteratively merge pairs of user nodes into supernodes based on the similarity of their rating profiles. The result is a summarized graph G′=(U′∪I,E′,w′,s′)G =(U ∪ I,E ,w ,s ) with |U′|<|U||U |<|U|, where each supernode S⊆US U represents a group of original users. The aggregated weight of supernode S toward item i is w′(S,i)=∑u∈S:(u,i)∈Ew(u,i)|u∈S:(u,i)∈E|,w (S,i)= _u∈ S:\,(u,i)∈ Ew(u,i)|\u∈ S:(u,i)∈ E\|, (5) when at least one member of S has rated i. The collective top-k ranking is then derived from G′G using the aggregation rules described in Section 2.2. The number of accepted merges is bounded by a merge budget expressed as a fraction of |U||U| rather than an absolute count, so that the same relative compression target applies regardless of dataset size; Section 5 reports a robustness sweep over this budget. EDI preservation constraints. A merge producing candidate summary G′G is accepted if and only if ΔE(G′) E(G ) ≤ΔE(G)+εE, ≤ E(G)+ _E, (6) ILD(G′) (G ) ≥ILD(G)−εD, (G)- _D, (7) inclusiong(G′) _g(G ) ≥inclusiong(G)−εI∀g, _g(G)- _I ∀\,g, (8) where εE,εD,εI≥0 _E, _D, _I≥ 0 are degradation tolerances controlling the trade-off between compression and EDI preservation. Formal objective. The overall problem is minG′ _G ℒ(G,G′) (G,G ) (9) s.t. .t. ΔE(G′)≤ΔE(G)+εE, E(G )≤ E(G)+ _E, ILD(G′)≥ILD(G)−εD, (G ) (G)- _D, inclusiong(G′)≥inclusiong(G)−εI∀g, _g(G ) _g(G)- _I ∀\,g, where ℒ(G,G′)L(G,G ) is the structural loss measured as the mean squared error between original and reconstructed edge weights. The tolerances are calibrated empirically from baseline measurements on the full graph, as described in Section 5. 4.3 Illustrative Example To illustrate concretely how unconstrained aggregation can harm EDI, consider four users — u1∈Fu_1 _F and u2,u3,u4∈Mu_2,u_3,u_4 _M — and three items, with ratings as shown in Table 1. This 1F:3M ratio mirrors the gender imbalance of the MovieLens 100k dataset (29% female, 71% male), our primary evaluation benchmark. Ranking items by average score yields i2≻i3≻i1i_2 i_3 i_1, because i1i_1 is rated 5 by u1u_1 but only 1 and 2 by two male users, pulling its mean down to 2.67. The top-2 recommendation R=i2,i3R=\i_2,i_3\ exposes a severe fairness problem. Computing the EDI metrics on R (with θ=4θ=4): utilityF(R) _F(R) =12(w(u1,i2)+w(u1,i3))=12(2+0)=1.0, = 12(w(u_1,i_2)+w(u_1,i_3))= 12(2+0)=1.0, utilityM(R) _M(R) =16∑j=24(w(uj,i2)+w(uj,i3))=266=4.33, = 16 _j=2^4(w(u_j,i_2)+w(u_j,i_3))= 266=4.33, ΔE(R) E(R) =|1.0−4.33|=3.33. =|1.0-4.33|=3.33. Moreover, u1u_1 finds no item in R with w(u1,i)≥4w(u_1,i)≥ 4, so inclusionF(R)=0<αF=0.25inclusion_F(R)=0< _F=0.25, while inclusionM(R)=0.83>αM=0.75inclusion_M(R)=0.83> _M=0.75: the female user is entirely excluded from the relevant items of the top-2 list. Had i1i_1 been included instead — R′=i1,i2R =\i_1,i_2\ — we would obtain ΔE(R′)=0.67 E(R )=0.67 and inclusionF(R′)=0.5≥αFinclusion_F(R )=0.5≥ _F: a substantially fairer outcome. Our EDI-constrained coarsening detects such distortions at the structural level: any merge of user nodes that would lead to recommending R over R′R is rejected, because it increases ΔE E beyond the tolerance εE _E. Table 1: Toy example: ratings (– denotes an unobserved entry). User Group i1i_1 i2i_2 i3i_3 u1u_1 F 5 2 – u2u_2 M 1 5 3 u3u_3 M – 4 5 u4u_4 M 2 5 4 5 Experimentation 5.1 Datasets We evaluate our approach across five datasets spanning four domains, covering both user-side and item-side equity settings. MovieLens 100k and 1M [4]. MovieLens 100k contains 100,000 ratings from 943 users on 1,682 movies (scale 1–5). Gender is the sensitive attribute on users: FG_F (273 female, 29%) and MG_M (670 male, 71%). MovieLens 1M extends this to 6,040 users, 3,706 movies, and 1,000,209 ratings, used for scalability validation. We set k∈5,10,20k∈\5,10,20\. libimseti.cz. A Czech social dating network where users rate other users on attractiveness. The sensitive attribute is the gender of the rating user (user-side equity). We set k∈5,10,20k∈\5,10,20\. Rate My Professors. An educational rating platform where students rate professors. The sensitive attribute is the gender of the professor (item-side equity). We set k∈5,10,20k∈\5,10,20\. OpenAlex (AI/ML/CS, 2018–2023). An academic authorship graph built from the OpenAlex API, comprising 99 venues, 904 authors (171 F / 733 M, αF≈19% _F≈ 19\%), and 2,124 ratings (co-authorship counts). Gender is inferred from author first names. The sensitive attribute is on items (item-side equity). We set k∈5,10,20k∈\5,10,20\. Table 2: Overview of the five datasets. Dataset Domain |U||U| |I||I| |E||E| Scale Equity αF _F MovieLens 100k Movies 943 1,682 100,000 1–5 user-side 29% MovieLens 1M Movies 6,040 3,706 1,000,209 1–5 user-side 28% libimseti.cz Dating 1,000 32,677 97,707 1–10 user-side 50% Rate My Prof. Academic 1,981 59,066 150,800 1–5 item-side 51%* OpenAlex Publications 99 904 2,124 1–5 item-side 19% * αF _F = proportion of women among the items (recommended professors), not among users. Figure 1: Overview of the five datasets: corpus size (log scale) and gender imbalance αF _F by equity side (top), and rating distribution for each dataset (bottom). For Rate My Professors, the rating is a continuous (course, professor) average on 1–5, grouped into eight bins of width 0.5. 5.2 Baselines We compare our EDI-constrained summarization against five baselines: (1) Average Score, which ranks items by their mean rating; (2) Borda Count, which converts each user’s ratings into ranks and sums them; (3) Weighted Borda, which normalizes Borda scores by group size to compensate for demographic imbalances; (4) Condorcet, which ranks items by pairwise majority preference; and (5) Fair Re-rank, a post-processing baseline that greedily re-ranks the top-40 Borda candidates to maximize the sum of group inclusion scores while minimizing the equity gap. None of the first four rules explicitly controls EDI during aggregation; Fair Re-rank addresses EDI as a post-hoc correction. 5.3 Evaluation Protocol We evaluate all methods on the EDI metrics defined in Section 4.1. For user-side equity datasets (MovieLens, libimseti), we report ΔE E, ILD, and group inclusion scores (incFinc_F, incMinc_M), with relevance threshold θ∈3.5,4.0θ∈\3.5,4.0\ for MovieLens and θ=7.0θ=7.0 for libimseti — the semantic equivalent of the MovieLens threshold on the platform’s 1–10 scale, rather than a strict linear rescaling. For item-side equity datasets (Rate My Professors, OpenAlex), we report ΔE E, ILD, and fracFfrac_F — the fraction of female items in the top-k list, with θ=4.0θ=4.0 for Rate My Professors (same 1–5 scale as MovieLens) and θ=1.0θ=1.0 for OpenAlex, a minimal threshold justified by the strong sparsity of the rating matrix (rating =min(papers,5)= (papers,5); most authors have only one paper per venue, see Figure 1). Degradation tolerances are set to εE=0.1 _E=0.1, εD=0.05 _D=0.05, and εI=0.05 _I=0.05, calibrated from baseline measurements on the full graph. We set k∈5,10,20k∈\5,10,20\ for all datasets, and report the compression ratio |U′|/|U||U |/|U| alongside all EDI metrics. 5.4 Results Tables 3–5 report the EDI metrics and compression ratio for all methods at k∈5,10,20k∈\5,10,20\ and θ=4.0θ=4.0. Table 3: EDI metrics at k=5k=5, θ=4.0θ=4.0. Bold: best value per column. αF=0.29 _F=0.29, αM=0.71 _M=0.71. Method ΔE↓ E ILD↑ incF↑inc_F incM↑inc_M Ratio↓ Average Score 0.008 1.000 0.001 0.002 – Borda 0.491 0.303 0.337 0.453 – Weighted Borda 0.491 0.303 0.337 0.453 – Condorcet 0.478 0.340 0.333 0.446 – Fair Re-rank 0.151 0.369 0.297 0.333 – AURORA 0.439 0.330 0.346 0.450 0.499 αg _g target – – 0.29 0.71 – Table 4: EDI metrics at k=10k=10, θ=4.0θ=4.0. Bold: best value per column. αF=0.29 _F=0.29, αM=0.71 _M=0.71. Method ΔE↓ E ILD↑ incF↑inc_F incM↑inc_M Ratio↓ Average Score 0.007 1.000 0.001 0.002 – Borda 0.452 0.349 0.287 0.393 – Weighted Borda 0.425 0.354 0.293 0.392 – Condorcet 0.446 0.356 0.292 0.394 – Fair Re-rank 0.162 0.429 0.271 0.313 – AURORA 0.423 0.391 0.307 0.405 0.499 αg _g target – – 0.29 0.71 – Table 5: EDI metrics at k=20k=20, θ=4.0θ=4.0. Bold: best value per column. αF=0.29 _F=0.29, αM=0.71 _M=0.71. Method ΔE↓ E ILD↑ incF↑inc_F incM↑inc_M Ratio↓ Average Score 0.056 0.956 0.034 0.045 – Borda 0.424 0.378 0.246 0.339 – Weighted Borda 0.388 0.376 0.250 0.336 – Condorcet 0.441 0.380 0.244 0.340 – Fair Re-rank 0.240 0.427 0.258 0.310 – AURORA 0.285 0.462 0.277 0.344 0.499 αg _g target – – 0.29 0.71 – Several observations emerge from these results. First, Average Score achieves the lowest ΔE E and highest ILD at all k values, but this is a degenerate outcome: it recommends identical items to all users regardless of group, producing near-zero inclusion for both groups. Second, Fair Re-rank consistently achieves the best ΔE E among competitive methods across all k, confirming that targeted post-processing can reduce the equity gap effectively. Third, our method beats all three classical voting rules (Borda, Weighted Borda, Condorcet) on ΔE E at every k, though it does not close the gap with Fair Re-rank; it also achieves the best inclusion score for at least one group at every k. At k=10k=10, AURORA and Condorcet each improve all four metrics over Borda simultaneously; Weighted Borda falls just short on incMinc_M, and Fair Re-rank, despite its large ΔE E advantage, trails Borda on both inclusion criteria. At k=20k=20 AURORA improves ΔE E, ILD, incFinc_F, and incMinc_M over Borda, Condorcet, and Weighted Borda simultaneously, without directly reweighting scores by group size the way Weighted Borda does. On ILD specifically, AURORA outperforms Borda and Condorcet at every k, with the single exception of k=5k=5, where Condorcet is marginally higher (0.340 vs. 0.330); against Fair Re-rank, AURORA’s advantage only materializes at k=20k=20 (0.462 vs. 0.427), while Fair Re-rank retains a higher ILD at k=5k=5 and k=10k=10. Finally, the compression ratio of our method is governed by the merge budget rather than by k: with a budget expressed as a fixed fraction of |U||U| (see Section 4.2), the graph is reduced to approximately 50% of its original size (471 supernodes) at every k∈5,10,20k∈\5,10,20\, a design choice we validate through a robustness sweep in Section 5.7. Figure 2: EDI metrics for all baselines at k∈5,10,20k∈\5,10,20\, θ=4.0θ=4.0. Lower ΔE E is better (equity); higher ILD is better (diversity); higher inclusion is better, with dashed lines marking the proportional targets αF=0.29 _F=0.29 and αM=0.71 _M=0.71. Table 6: Average execution time (seconds) per method and list size k, measured on MovieLens 100k (θ=4.0θ=4.0, averaged over 3 runs). Method k = 5 k = 10 k = 20 Average Score 0.005 s 0.004 s 0.004 s Borda 0.720 s 0.677 s 0.666 s Weighted Borda ∼0.72 0.72 s ∼0.68 0.68 s ∼0.67 0.67 s Condorcet 0.149 s 0.129 s 0.126 s Fair Re-rank 0.938 s 0.928 s 0.926 s AURORA 3.793 s 3.761 s 4.042 s Computational efficiency. Table 6 reports execution times per method. All baselines complete in under one second. Because the merge budget is expressed as a fixed fraction of |U||U| rather than a fixed absolute count, the number of candidate merges the algorithm evaluates no longer depends on k, and AURORA’s runtime is stable across k∈5,10,20k∈\5,10,20\ (3.8–4.0 s on MovieLens 100k). This is roughly 44–6×6× slower than Fair Re-rank and 55–6×6× slower than Borda, but remains on the order of a few seconds even as the dataset grows (Section 5.8), which we consider acceptable given that coarsening is typically performed offline. 5.5 Multi-Domain Evaluation Tables 7–10 extend the evaluation to the three additional datasets. On libimseti (Table 7, θ=7.0θ=7.0 on the platform’s 1–10 rating scale), Average Score achieves both the lowest ΔE E (0.016) and the highest ILD (0.867), again by recommending the same globally popular profiles to every rater regardless of group. Borda-based methods and AURORA all produce equity gaps above 1.2, whereas Fair Re-rank (0.139) is a clear outlier among the non-degenerate methods. AURORA achieves the best ILD among all methods that produce non-trivial inclusion (0.761, ahead of Borda, Weighted Borda, and Condorcet, which range from 0.716 to 0.746), but does not reduce ΔE E relative to Borda. We analyze this limitation in detail in Section 5.6: unlike the other three datasets, libimseti is the only corpus where the sensitive attribute is present on both sides of the bipartite graph, and we show that the persistently high ΔE E reflects a genuine difference in rating behavior between groups rather than an algorithmic shortcoming that compression could fix. A robustness sweep over the merge budget (30%–60% of |U||U|) confirms that this limitation is not a matter of under- or over-compression: ΔE E remains high across the whole range without approaching the reduction seen on the other three datasets. This holds at k=5k=5 and k=20k=20 too, except that at k=5k=5 Fair Re-rank alone dominates on both axes (ΔE=0.0004 E=0.0004, ILD=0.762=0.762), while at k=20k=20 its edge shrinks sharply (ΔE=0.315 E=0.315) as AURORA takes the diversity lead (ILD=0.781=0.781). On Rate My Professors (Table 9), AURORA achieves the second-highest intra-list diversity (ILD == 0.808, behind only Average Score’s 0.982) together with the highest female professor representation (fracF=0.60frac_F=0.60) among all methods. This comes at a moderate cost on equity: AURORA’s ΔE E (0.112) is higher than Borda’s (0.065) and further from the near-zero gap achieved by Average Score, Weighted Borda, and Fair Re-rank (all 0.000), so the method should be read as trading a real amount of equity for a large gain in diversity and representation on this dataset. Fair Re-rank raises fracFfrac_F to 0.50 but at the cost of dramatically lower diversity (ILD == 0.276), confirming that post-hoc re-ranking cannot jointly optimize diversity and item-side inclusion the way structural coarsening does. This trade-off shifts with k: at k=5k=5, AURORA has the only non-zero ΔE E (0.042) but by far the best representation (fracF=0.80frac_F=0.80); at k=20k=20, Borda instead has the worst ΔE E (0.139), which AURORA (0.078) beats while keeping the best ILD (0.818). On OpenAlex (Table 10), the item-side imbalance is stark: Borda, Weighted Borda, and Condorcet all recommend zero female authors (fracF=0.00frac_F=0.00) despite women representing 19% of the author pool. Average Score and Fair Re-rank both reach fracF=0.20frac_F=0.20, while our method achieves the lowest equity gap (ΔE=0.031 E=0.031, a 56% improvement over Average Score’s 0.071) while maintaining comparable female representation (fracF=0.194frac_F=0.194). Here, unlike on RMP, AURORA improves equity and maintains diversity simultaneously, confirming that EDI-constrained graph coarsening generalizes meaningfully to item-side equity settings, though its benefits are domain-dependent rather than uniform: the bias stays severe at all three k tested — at k=5k=5 even Average Score fails (ΔE=1.23 E=1.23) for lack of candidates to dilute it, and at k=20k=20 Borda’s bias only eases slightly (ΔE=0.907 E=0.907, 5% female authors); AURORA keeps the lowest ΔE E throughout (0.058 at k=5k=5/20, 0.031 at k=10k=10). Table 7: EDI metrics on libimseti.cz (k=10k=10, user-side equity, θ=7.0θ=7.0 on the platform’s 1–10 scale). Bold: best per column. Method ΔE↓ E ILD ↑ incF↑inc_F incM↑inc_M Average Score 0.016 0.867 0.002 0.000 Borda 1.301 0.716 0.143 0.024 Weighted Borda 1.301 0.716 0.143 0.024 Condorcet 1.296 0.746 0.157 0.024 Fair Re-rank 0.139 0.716 0.038 0.024 AURORA 1.232 0.761 0.148 0.024 5.6 Why ΔE E Remains High on libimseti On the three other datasets, the sensitive attribute lives on only one side of the bipartite graph: gender is a property of users on MovieLens, and a property of items on Rate My Professors and OpenAlex. libimseti is different: both the raters and the rated profiles carry a gender label, because the items being recommended are themselves people. To understand why AURORA, like the voting rules, does not reduce ΔE E on this dataset, we cross-tabulate the mean rating by the gender pair (rater, rated profile) across the full 17.3M-edge libimseti graph (12,258,052 ratings with gender known on both sides), shown in Table 8. Table 8: Mean rating by rater–profile gender pair on libimseti.cz (1–10 scale, full graph). Rater → Rated Mean rating # ratings F → M 6.92 7,099,688 M → F 5.48 3,232,064 F → F 5.14 1,243,590 M → M 4.46 682,710 The gap between the highest mean rating (F→ , 6.92) and the lowest (M→ , 4.46) is large and consistent across more than 12 million ratings: it is a structural property of the data, not statistical noise. A single collective ranking, shared by every rater regardless of group, cannot simultaneously satisfy raters whose underlying rating distributions differ this much. This explains two observations from Table 7: first, ΔE E is elevated for the voting methods (Borda, Weighted Borda, Condorcet) and for AURORA alike — Average Score and Fair Re-rank are the exceptions, but only because neither produces a ranking that differentiates between groups in the first place; second, the EDI-preservation constraint on the coarsening process has essentially no effect here, since the top-k list is already dominated by profiles that are highly rated across the board, and merging users of the same gender cannot transfer information about a group’s preferences for items it rates comparatively lower. This result is an empirical illustration of an argument made by Yao and Huang [14]: demographic parity (ΔE≈0 E≈ 0) is not always an appropriate fairness target when the preferences of different groups genuinely diverge. On MovieLens or Rate My Professors, nothing about the domain suggests that a user’s gender should influence how much they enjoy a film or how highly they rate a professor’s teaching, so a persistent ΔE E gap there is plausibly attributable to the aggregation rule. On libimseti, by contrast, the sensitive attribute enters the preference signal itself through the structure of romantic and social attraction, so a high ΔE E may reflect a genuine difference in preference rather than an unfair outcome to correct. We verified that this is not a matter of under-calibration: across the same merge-budget sweep described in Section 5.7 (30%–60% of |U||U|), ΔE E remains elevated throughout, while AURORA’s diversity advantage over the voting methods persists regardless of budget. We view the elevated ΔE E as a genuine limitation of a single-ranking aggregation framework on domains with reciprocal, attribute-dependent preferences, rather than a defect specific to our coarsening method. Table 9: EDI metrics on Rate My Professors (k=10k=10, item-side equity). fracFfrac_F = fraction of female professors in top-k. Bold: best per column. Method ΔE↓ E ILD ↑ fracF↑frac_F Average Score 0.000 0.982 0.40 Borda 0.065 0.267 0.50 Weighted Borda 0.000 0.245 0.20 Condorcet 0.076 0.253 0.30 Fair Re-rank 0.000 0.276 0.50 AURORA 0.112 0.808 0.60 Table 10: EDI metrics on OpenAlex AI/ML/CS 2018–2023 (k=10k=10, item-side equity; αF≈19% _F≈ 19\%). Bold: best per column. Method ΔE↓ E ILD ↑ fracF↑frac_F Average Score 0.071 0.356 0.200 Borda 1.233 0.000 0.000 Weighted Borda 1.233 0.000 0.000 Condorcet 1.233 0.000 0.000 Fair Re-rank 0.071 0.356 0.200 AURORA 0.031 0.345 0.194 5.7 Robustness to the Merge Budget The merge budget (Section 4) is set to 50% of |U||U| throughout the main experiments. To check that this choice is not a narrow, cherry-picked setting, we re-run AURORA at four budgets — 30%, 42.4%, 50%, and 60% of |U||U| — on MovieLens 1M and Rate My Professors, the two datasets where the effect of compression is most visible. Table 11 reports ΔE E and ILD at each budget. Table 11: AURORA’s ΔE E and ILD across four merge budgets. MovieLens 1M at k=20k=20; Rate My Professors at k=10k=10. Budget (%\% of |U||U|) MovieLens 1M (k=20k=20) Rate My Professors ΔE↓ E ILD ↑ ΔE↓ E ILD ↑ 30% 0.332 0.456 0.112 0.745 42.4% 0.277 0.456 0.071 0.788 50% 0.277 0.456 0.112 0.808 60% 0.185 0.470 0.112 0.767 On MovieLens 1M, AURORA beats Borda, Weighted Borda, and Condorcet on both ΔE E and ILD at every budget in this range, and both metrics improve slightly as the budget grows — the method is robust to the exact choice of budget, and 50% is a reasonable, round value within a range that performs consistently well. On Rate My Professors, ILD is stable and consistently high (0.75–0.81) across the range, confirming that the diversity gain is not an artefact of the specific 50% budget; ΔE E, by contrast, does not vary smoothly with the budget and is not monotonically improved by more or less compression, which we attribute to the coarse granularity of a k=10k=10 ranking (only a limited number of distinct top-k configurations are reachable as merges accumulate). Borda remains close to ΔE≈0.065 E≈ 0.065 throughout this range on Rate My Professors, so the equity trade-off described in Section 5.4 holds regardless of the exact budget chosen. We did not observe a budget within 30–60% that closes this gap while preserving AURORA’s diversity advantage, which we leave as an open question for future calibration work (Section 6). Are the MovieLens 100k results at k=10k=10 (Table 2) stable under resampling of the user set? Subsampling without replacement (90% of |U||U|, 30 repetitions) confirms they are: AURORA beats Borda and Condorcet on ΔE E in 28/30 draws and on ILD in 30/30 draws (Weighted Borda: 24/30 and 30/30), with low variance on both metrics (ΔE=0.417±0.035 E=0.417± 0.035, ILD =0.391±0.004=0.391± 0.004) — AURORA’s advantage over the classical voting rules is not an artefact of the single draw reported in Table 2. Fair Re-rank, by contrast, stays ahead of AURORA on both metrics in all 30 draws without exception, confirming that its advantage on this dataset is likewise robust. Cross-Domain Summary Table 12 summarizes the best-performing method per metric and dataset at k=10k=10 (or the reported k for single-k datasets), excluding Average Score where it is degenerate. AURORA leads on diversity on MovieLens 100k and on both diversity and representation on the item-side datasets (RMP, OpenAlex), and it beats every classical voting rule on ΔE E across all five datasets. It is not, however, the strongest method everywhere: Fair Re-rank achieves the best ΔE E among non-degenerate methods on MovieLens 100k and, notably, both the best ΔE E and the best ILD on MovieLens 1M, making it the overall strongest method on that dataset rather than AURORA. No single method wins across all metrics and domains, which confirms that EDI objectives are in tension and that no single mechanism — structural or post-hoc — dominates uniformly across settings. Table 12: Cross-domain summary: best method per metric at k=10k=10 (or the single reported k for libimseti, RMP, OpenAlex). Dataset Best ΔE E Best ILD Best inc/fracF Overall ML 100k Fair Re-rank Fair Re-rank AURORA AURORA (k=20k=20) ML 1M Fair Re-rank Fair Re-rank Fair Re-rank Fair Re-rank libimseti Fair Re-rank AURORA Condorcet None (persistent gap) RMP Avg Score / W.Borda / F.R. Avg Score AURORA Trade-off: AURORA (div.) / F.R. (eq.) OpenAlex AURORA Avg Score / F.R. Avg Score / F.R. AURORA ∗Average Score is excluded above wherever it is degenerate on inclusion (near-zero incFinc_F/incMinc_M): on the three user-side datasets — ML 100k, ML 1M, and libimseti alike — recommending the same list to every user regardless of group leaves it with almost no group-specific relevant items. On the two item-side datasets (RMP, OpenAlex), fracFfrac_F is not similarly degenerate for Average Score, so it is not excluded there. F.R. = Fair Re-rank; AURORA is a close third on OpenAlex ILD and fracFfrac_F. 5.8 Scalability To assess whether EDI-constrained coarsening scales beyond MovieLens 100k, we evaluate all methods on MovieLens 1M (6,040 users, 3,706 items, 1,000,209 ratings) at k∈5,10,20k∈\5,10,20\ and θ=4.0θ=4.0. Table 13 reports results at k=10k=10. Table 13: EDI metrics on MovieLens 1M (k=10k=10, θ=4.0θ=4.0). Bold: best per column. Method ΔE↓ E ILD ↑ incF↑inc_F incM↑inc_M Average Score 0.000 1.000 0.000 0.000 Borda 0.482 0.418 0.305 0.409 Weighted Borda 0.414 0.426 0.311 0.400 Condorcet 0.487 0.408 0.305 0.412 Fair Re-rank 0.019 0.452 0.336 0.343 AURORA 0.214 0.440 0.321 0.370 The relative ordering among the classical voting rules is broadly consistent with MovieLens 100k: Weighted Borda improves over Borda on ΔE E (0.482 → 0.414 at k=10k=10), and AURORA beats all three voting rules (Borda, Weighted Borda, Condorcet) on both ΔE E and ILD at every k∈5,10,20k∈\5,10,20\. However, unlike on MovieLens 100k, Fair Re-rank dominates AURORA on both ΔE E and ILD at every k on this larger dataset (e.g. at k=10k=10: ΔE=0.019 E=0.019 and ILD=0.452=0.452 for Fair Re-rank, versus 0.214 and 0.440 for AURORA). We attribute this to the larger user base making the post-hoc re-ranking baseline more effective: with 6,040 users to draw candidates from, Fair Re-rank’s greedy re-ranking of the top-40 Borda candidates has considerably more room to satisfy both groups than on the 943-user MovieLens 100k graph. AURORA’s most distinctive result on 1M is at k=20k=20, where it remains competitive on incFinc_F (0.294, within 0.001 of the best, Weighted Borda at 0.295, and ahead of Fair Re-rank at 0.291), suggesting that its advantage is concentrated in balancing inclusion across groups rather than in minimizing ΔE E or maximizing ILD outright at this scale. Figure 3 shows the side-by-side comparison of ΔE E and ILD across all methods at k∈10,20k∈\10,20\. Figure 3: Side-by-side comparison of ΔE E and ILD between MovieLens 100k and 1M, for all six methods at k∈10,20k∈\10,20\ (top row: k=10k=10; bottom row: k=20k=20). Lighter bars denote MovieLens 100k, darker bars denote MovieLens 1M. 6 Conclusion and Future Work This paper addressed the problem of aggregating user preferences in a way that explicitly preserves equity, diversity, and inclusion. We represented preferences as a weighted attributed bipartite graph and proposed AURORA, an EDI-constrained coarsening algorithm that embeds fairness directly into the graph structure: each candidate merge of user nodes is accepted only if the resulting summarized graph maintains the equity gap, intra-list diversity, and group inclusion of the original within prescribed tolerances. This structural approach contrasts with existing post-hoc techniques such as re-ranking, which enforce fairness after the aggregation has already been computed. Evaluated across five datasets spanning four domains, no single baseline satisfies all three EDI criteria simultaneously. On MovieLens 100k, AURORA consistently beats the classical voting rules (Borda, Weighted Borda, Condorcet) on both equity and diversity across k∈5,10,20k∈\5,10,20\, with a merge budget robust across a 30–60% range; Fair Re-rank remains the most accurate on equity alone, at some cost to diversity. This picture is dataset-dependent rather than universal: on the larger MovieLens 1M, Fair Re-rank dominates AURORA on both axes, which we attribute to its larger candidate pool for re-ranking; on libimseti, where the sensitive attribute sits on both sides of the bipartite graph, AURORA — like the classical voting rules — does not reduce the equity gap, a limitation traced to a genuine difference in rating behavior between groups rather than an algorithmic shortcoming. On the item-side datasets, AURORA shows two distinct patterns: on Rate My Professors it trades equity for a large gain in diversity (ILD == 0.808) and female representation (fracF=60%frac_F=60\%), while on OpenAlex it improves equity and maintains diversity simultaneously, reaching the lowest equity gap observed across all five datasets (ΔE=0.031 E=0.031) and correcting the most extreme bias in our evaluation. Taken together, these results support a more precise claim than "AURORA is uniformly better": embedding EDI constraints into the coarsening structure consistently outperforms unconstrained voting rules, and matches or improves on post-hoc re-ranking on smaller or item-side datasets, but a sufficiently large user base or a domain with reciprocal, attribute-dependent preferences can favor a post-hoc approach or expose a genuine limit of any single-ranking aggregation framework. This nuance is itself a contribution: it clarifies the conditions under which structural, constraint-based summarization is preferable to re-ranking, rather than asserting unconditional superiority. Several directions remain open for future work: extending the framework to multiple simultaneous sensitive attributes (e.g., gender combined with age or occupation); adapting the static coarsening process to dynamic or streaming preference graphs; deriving the tolerances εE _E, εD _D, εI _I and the merge budget from a principled criterion — such as a Pareto-frontier analysis or a held-out validation split — rather than an empirical robustness sweep; understanding why Fair Re-rank overtakes AURORA on MovieLens 1M but not on smaller datasets, to clarify the boundary conditions favoring each mechanism; on Rate My Professors specifically, designing a merge criterion that accounts for the downstream item distribution rather than rating-profile similarity alone, to narrow the equity–diversity trade-off without sacrificing representation gains; and replacing the greedy merge strategy with community-detection techniques guided directly by the EDI impact of each candidate merge. References [1] A. Aird, C. All, P. Farastu, E. Stefancova, J. Sun, N. Mattei, and R. Burke (2023) Exploring social choice mechanisms for recommendation fairness in scruf. External Links: Link Cited by: §3.4. [2] A. Aird, E. Štefancová, C. All, A. Voida, M. Homola, N. Mattei, and R. Burke (2024) Social choice for heterogeneous fairness in recommendation (scruf-d). External Links: Link Cited by: §3.4, §4.1, §4.1. [3] Y. Dong, J. Ma, S. Wang, C. Chen, and J. Li (2023) Fairness in graph mining: a survey. IEEE Transactions on Knowledge and Data Engineering 35, p. 10583–10602. External Links: Link, Document Cited by: §3.3. [4] F. M. Harper and J. A. Konstan (2015) The MovieLens datasets: history and context. ACM Transactions on Interactive Intelligent Systems 5 (4), p. 1–19. External Links: Document Cited by: §1, §5.1. [5] F. Kamiran and T. Calders (2012) Data preprocessing techniques for classification without discrimination. Knowledge and Information Systems 33 (1), p. 1–33. External Links: Document Cited by: §1. [6] L. Kellerhals and J. Peters (2024) Proportional fairness in clustering: a social choice perspective. arXiv (en). Note: arXiv:2310.18162 [cs.LG] External Links: Link, Document Cited by: §3.1, §4.1. [7] J. Leonhardt, A. Anand, and M. Khosla (2018) User fairness in recommender systems. External Links: Link Cited by: §3.3. [8] Y. Liu, T. Safavi, A. Dighe, and D. Koutra (2018) Graph summarization methods and applications: a survey. arXiv (en). Note: arXiv:1612.04883 [cs.IR] External Links: Link, Document Cited by: §1, §2.3, §3.2. [9] N. Mehrabi, F. Morstatter, N. Saxena, K. Lerman, and A. Galstyan (2021) A survey on bias and fairness in machine learning. ACM Computing Surveys 54 (6), p. 1–35. External Links: Document Cited by: §1. [10] F. Ricci, L. Rokach, and B. Shapira (2011) Introduction to recommender systems handbook. In Recommender Systems Handbook, p. 1–35. External Links: Document Cited by: §2.2. [11] S. B. Roy, B. Schieber, and N. Talmon (2024) Fairness in preference queries: social choice theories meet data management. Proceedings of the VLDB Endowment 17 (12), p. 4225–4228 (en). External Links: ISSN 2150-8097, Link, Document Cited by: §3.1. [12] N. Shabani, J. Wu, A. Beheshti, Q. Z. Sheng, J. Foo, V. Haghighi, A. Hanif, and M. Shahabikargar (2024) A comprehensive survey on graph summarization with graph neural networks. arXiv (en). Note: arXiv:2302.06114 [cs.LG] External Links: Link, Document Cited by: §3.2. [13] A. Singh and T. Joachims (2018) Fairness of exposure in rankings. In Proceedings of the 24th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, p. 2219–2228. External Links: Document Cited by: §1. [14] S. Yao and B. Huang (2017) New fairness metrics for recommendation that embrace differences. External Links: Link Cited by: §3.3, §4.1, §5.6. [15] Y. Zhao, Y. Wang, Y. Liu, X. Cheng, C. C. Aggarwal, and T. Derr (2024) Fairness and diversity in recommender systems: a survey. ACM Transactions on Intelligent Systems and Technology 16. External Links: Link, Document Cited by: §1, §3.3.