From Network Inequality to Network Fairness: A Perspective on Responsible Decision-Making
Authors: Lisette Espín-Noboa, Tina Eliassi-Rad, Pak-Hang Wong, Erich Prem, Meike Zehlike, Ricardo Baeza-Yates, Suresh Venkatasubramanian, Fariba Karimi
Organizations: Complexity Science Hub Vienna, Vienna, Austria · Northeastern University, Boston, USA · Santa Fe Institute, Santa Fe, USA · Hong Kong Baptist University, Kowloon Tong, Hong Kong · Vienna University of Technology, Vienna, Austria · KTH Royal Institute of Technology, Stockholm, Sweden · Universitat Pompeu Fabra, Barcelona, Spain · Brown University, Providence, USA · Graz University of Technology, Graz, Austria
Social networks shape how individuals make decisions and how opportunities are distributed. However, the mechanisms that generate these networks often reflect pre-existing inequalities, and technologies that rely on network-derived signals risk further amplifying such disparities. Algorithmic fairness research largely treats networks as a fixed background, grounding analysis almost exclusively in distributive justice and overlooking how network structures systematically bias decision-making. In this Perspective, we identify ten network effects and trace how they create structural biases in the relationship between what we intend to measure and what we observe. Using academic hiring as an example, we show that network biases are not inherently harmful or beneficial. Determining their legitimacy requires examining the entire decision-making process through the lenses of both distributive and procedural justice while engaging all affected stakeholders. We therefore call for a holistic, networked approach to fairness that moves beyond static group categories and recognizes the dynamic, relational, and structural nature of inequality.
Figures & tables
#
Network effect
Mechanism
Structure involved
Example
Node-level effects
1
Rich-get-richer effect
preferential attachment
node degree
When eminent scientists get disproportionately more credit for their contributions to science while relatively unknown scientists tend to get disproportionately less credit for comparable contributions. [ 38 ]
2
First-mover advantage
non-Markovian temporal process
node degree and age
When the first papers in a field, essentially regardless of content, receive citations at a higher rate than papers published later. [ 39 , 40 ]
3
In-group favoritism
homophily
node attributes
When male workers who have male supervisors have higher chances of promotion than their female counterparts, or vice versa. [ 41 ]
Neighborhood-level effects
4
Guilt-by-association
homophily
1-hop neighborhood
In P2P lending, when the credit score of a person is defined by (the credit score of) her friends regardless of her own credit history. [ 42 , 43 ]
Table 1: Taxonomy of network effects. Ten effects that drive inequality in network-mediated decisions, organized by structural scope: node-level, neighborhood-level, and structural-level.
Figure 1: Biases in social decision-making processes . A) Spaces: The construct space encapsulates unmeasurable ideals, while the observed space employs measurable proxies of the constructs, affected by underlying structural biases . Acknowledging these biases requires adopting the “we-are-all-equal” (WAE) worldview, focusing on group fairness or non-discrimination. [ 65 ] We argue that the structural biases reflect a complex interplay between imbalanced group representations and biases rooted in personal and social networks . Feedback loops can further amplify these biases in the observed space. B) Transformations: A vertical transformation represents the decision-making process where input features F∙ fuel an algorithm A∙ , yielding outputs or decisions D∙ that reflect underlying rules or learned patterns. A horizontal transformation reflects the process of converting construct variables ( ∙c ) into observed variables ( ∙o ). [ 66 ] We argue that personal and social networks significantly influence the entire decision-making pipeline ( F∙→D∙ and ∙c→∙o ), impacting both individual and group fairness . C) Network bias anatomy: Nodes, edges, and network structure act as indicators of individual importance, influencing decision-making processes and contributing to social inequalities. D) Application to academic hiring. Construct-space variables (Expertise, Evaluation, Best candidate) are transformed through structural biases into observed proxies (h-index, Ranking, Top-1). These biases include not only those traditionally studied in fairness (e.g., historical and gender bias) but also network-based biases, which can be advantageous (e.g., the chaperone effect from a prestigious coauthor) or detrimental (e.g., guilt-by-association from being connected to an unethical supervisor). While prior research mainly examines individual and group fairness, we advocate for a holistic and comprehensive approach that also considers network effects.
Figure 2: Network signals can override bibliometrics in academic hiring decisions. A) Schematic of the academic hiring process. Candidates are evaluated through bibliometric indicators (e.g., citations) and recommendation letters, where each letter is weighted by the hiring committee’s trust in the referee. Together, these observable features serve as proxies for latent candidate fit and are combined by a decision algorithm to produce a hiring outcome. B) Likelihood distributions of network and citation signals for good and bad candidates (derived from a Bayesian model; Appendix A ). Network signals provide stronger discriminability between candidate types ( d′=3.68 ) than citation counts ( d′=2.42 ), suggesting that social capital is a more informative cue than bibliometric output in this model. C) Posterior probability of being a good candidate as a function of both signals. Contour lines indicate constant posterior levels. Highlighted regions correspond to candidates achieving similarly high posterior probabilities through different signal combinations: (a) strong network and bibliometric signals, (b) strong network but weak bibliometric signal, and (c) strong bibliometric but moderate network signal. Region (b) illustrates that network signals can override weak bibliometric performance, while region (c) shows the opposite. Overall, these regions demonstrate that a high probability of candidate fit can arise from trade-offs across signal dimensions, not only from strength in both.
Appendix figures & tables8 assets
Supplementary material from the paper’s appendix.
Appendix
Component
Parameter
Value
Prior
P(good)
0.35
Payoffs
hire good or reject bad
0
hire bad
−50
reject good
−100
Network: referral quality
aggregation
sum over 3 letters
reference score (numeric)
excellent 5 , good 4 , average 3 , bad 2 , very_bad 1
Appendix
Table A.1 : Simulation parameters for the Bayesian hiring model. Parameter values used throughout all simulations. The prior P(good)=0.35 reflects an assumption that good candidates are a minority of the applicant pool. Payoffs are defined asymmetrically: missing a good candidate (reject good: −100 ) is penalized twice as heavily as hiring a bad one (hire bad: −50 ), while correct decisions carry no cost. The network signal is computed as the sum of score×trust across three recommendation letters, where reference scores and trust weights follow stylized discrete distributions that differ markedly between good and bad candidates. Bibliometric signals are modeled using standard count distributions: citation counts follow log-normal distributions (capturing the heavy-tailed nature of citation data), publication counts follow Poisson distributions, and h-index values follow truncated power laws—all with parameters chosen to produce realistic but clearly separated distributions between good and bad candidates.
Figure A.1 : Generative model of the network signal and its discriminability between good and bad candidates. A) Likelihood distributions of the two components of the network signal, conditioned on candidate fit. Reference score (left) ranges from very bad (1) to excellent (5); trust weight (right) ranges from untrustworthy (-1) to trustworthy (1). Trust weight is a more discriminative signal than reference score alone ( d′=2.09 vs. 0.76 , respectively). B) Likelihood of the aggregate network signal, computed as ∑iscorei×trusti across three recommendation letters. Combining both components substantially improves discriminability ( d′=3.68 ). C) Posterior probability P(good∣x) given the aggregate network signal alone, using prior P(good)=0.35 . The steep sigmoidal curves confirm that the aggregate signal is a highly informative cue for candidate quality, and forms the basis of the network signal used throughout the paper.
Figure A.2 : Generative model of the non-network signal and posterior distributions. Each row corresponds to a different bibliometric: number of citations (log-normal, top—used in the main text), number of publications (Poisson, middle), and h-index (power law, bottom). A) Likelihood P(x∣good/bad) ; good candidates tend toward higher values in all three metrics. B) One-dimensional posterior P(good∣x) using only the non-network signal, with prior P(good)=0.35 . C) Two-dimensional posterior P(good∣network,non-network) combining both signals. Contours show how a strong network signal can compensate for a weaker bibliometric record, and vice versa. The network signal model is the same as in Figure A.1 .
Figure A.3 : Simulated candidates and decision boundaries. Each panel shows simulated good (green + ) and bad (red × ) candidates as a function of referral quality (y-axis) and a bibliometric signal (x-axis): citations (left), publications (middle), and h-index (right). The solid curve marks the posterior-based boundary ( p≥0.5 ); the dashed curve the payoff-optimal boundary ( p≥0.33 ), derived under an asymmetric payoff structure in which rejecting a good candidate is twice as costly as hiring a bad one ( Section A.2.3 ). The gap between the two curves identifies candidates the payoff rule would advance but the posterior rule would not. The dotted rectangle marks the top-right heuristic, which requires both signals to fall within the top 20% of their respective value ranges.
Observed signals
Posterior-based
Payoff-based
Top-right rule
(net., non-net.)
good / bad
good / bad
good / bad
referral_quality, n_citations
350 / 650
352 / 648
4 / 996
referral_quality, n_publications
349 / 651
349 / 651
7 / 993
referral_quality, h_index
351 / 649
364 / 636
1 / 999
Appendix
Table A.2 : Number of candidates classified as good or bad under three decision rules. Each row combines referral quality (network) with one bibliometric measure. Out of 1,000 simulated candidates, the posterior- and payoff-based rules classify roughly 350 as good, consistent with the prior P(good)=0.35 . The top-right rule (top 20%) classifies nearly all candidates as bad, reflecting its strict requirement for high values on both signal dimensions simultaneously.
Observed signals
Accuracy ↑
Precision ↑
Recall ↑
1D Accuracy ratio
Realized ↑
(net., non-net.)
post. / pay. / topk
post. / pay. / topk
post. / pay. / topk
post. / pay. / topk
payoff
referral_quality, n_citations
1.00 / 0.99 / 0.66
0.99 / 0.99 / 1.00
0.99 / 0.99 / 0.01
0.99 / 0.99 / 1.35
− 450
referral_quality, n_publications
1.00 / 1.00 / 0.66
1.00 / 1.00 / 1.00
1.00 / 1.00 / 0.02
0.97 / 0.97 / 1.33
− 150
referral_quality, h_index
0.96 / 0.96 / 0.65
0.93 / 0.92 / 1.00
0.94 / 0.96 / 0.00
1.39 / 1.52 / 1.37
− 2,700
Appendix
Table A.3 : Classification performance of three decision rules across signal pairs. Results are shown as posterior (post.) / payoff-optimal (pay.) / top-20% of the value range (topk) for 1,000 simulated candidates. Bold denotes the best scores per decision rule and signal pair. The 1D accuracy ratio compares network-only to non-network-only accuracy; values >1 ( blue ) indicate that the network signal is more informative in isolation. Realized payoff is computed under the payoff-optimal rule using the payoffs in Table A.1 .
Figure B.1 : Two focus-group tasks in the social capital–skills space. Axes: “Social capital” (network-based signals) and “Skills” (non-network metrics). A) Whom would you hire? Four candidate profiles (P1–P4), one per quadrant. Participants ranked them for hiring. B) Minimum levels required. Empty grid shown to participants who had to place the minimum-required profile anywhere in the space for each role (PhD student, postdoc, professor).
Figure B.2 : Minimum required skills and social capital by role and focus group. Each column corresponds to a role (PhD student, postdoc, professor); each row (A-C) to one of the three focus groups (Vienna, Budapest, and Graz, respectively) with sample size n as indicated. Points are individual participants’ stated minimum thresholds on the two axes (0–100); dashed lines show the mean skills and mean social capital per group and role. Across all three groups, mean requirements increase with seniority: participants demand higher minimum skills and higher minimum social capital for a professor than for a postdoc, and higher for a postdoc than for a PhD student, illustrating context-dependent relaxation of the “top-right” bar.
Algorithmic fairness studies how automated decisions distribute errors, opportunities, and harms across groups, and how to measure and reduce disparities.
In the presence of feedback loops, algorithmic decisions at one time step can influence observed data in subsequent steps, potentially introducing selection bias or shifts in data distribution. Research has demonstrated that ignoring these effects can lead to unfairness, which may worsen over time as the model remains deployed within society. This raises important questions of how to measure and ensure fairness of algorithmic decision-making models over time. In this short paper, we present a taxonomy that distinguishes between different types of static and temporal fairness notions in recent advancements. We then suggest prospects for future research by identifying common implicit temporal assumptions, open questions to enhance our temporal understanding of fairness, and other open challenges.
Fairness in algorithmic decision-making is often defined in the predictive space, where predictive performance - used as a proxy for decision-maker (DM) utility - is traded off against prediction-based fairness notions, such as demographic parity or equality of opportunity. This perspective, however, ignores how predictions translate into decisions and ultimately into utilities and welfare for both DM and decision subjects (DS), as well as their allocation across social-salient groups. In this paper, we propose a multi-stakeholder framework for fair algorithmic decision-making grounded in welfare economics and distributive justice, explicitly modeling the utilities of both the DM and DS, and defining fairness via a social planner's utility that captures inequalities in DS utilities across groups under different justice-based fairness notions (e.g., Egalitarian, Rawlsian). We formulate fair decision-making as a post-hoc multi-objective optimization problem, characterizing the achievable performance-fairness trade-offs in the two-dimensional utility space of DM utility and the social planner's utility, under different decision policy classes (deterministic vs. stochastic, shared vs. group-specific). Using the proposed framework, we then identify conditions (in terms of the stakeholders' utilities) under which stochastic policies are more optimal than deterministic ones, and empirically demonstrate that simple stochastic policies can yield superior performance-fairness trade-offs by leveraging outcome uncertainty. Overall, we advocate a shift from prediction-centric fairness to a transparent, justice-based, multi-stakeholder approach that supports the collaborative design of decision-making policies.
Kavya Gupta, Nektarios Kalampalikis, Christoph Heitz +1
Department of Computer Science, Saarland University, Germany · Zurich University of Applied Sciences, Switzerland
Network embedding methods learn low-dimensional representations of graph-structured data to support downstream tasks such as node classification, link prediction, and influence maximization. However, real-world networks often reflect structural inequalities arising from demographic imbalances, homophily, and other societal biases, which fairness-agnostic embedding methods can encode and amplify. To address this issue, numerous fairness-aware network embedding methods have been proposed to mitigate bias while preserving embedding utility. This survey presents a comprehensive overview of fairness-aware network embeddings for complex networks. We propose a taxonomy that categorizes existing methods along three main complementary dimensions: underlying embedding approach (spectral, random walk, graph neural network, Bayesian, and method-agnostic), fairness intervention strategy (pre-processing, in-processing, and post-processing), and fairness objective criterion (embedding- or task-level). We further compare methods with respect to group versus individual fairness and assumptions regarding sensitive attributes. Finally, we discuss current limitations and highlight promising future research directions. This survey provides a unified perspective on fairness-aware network embedding and serves as a reference for developing fair and trustworthy network representation learning methods.
Ella Has, Harshith Kumar Yadav, Gaurav Dixit +2
LIACS, Leiden University Leiden, The Netherlands · Dept. of Computer Science IIT Ropar, India · Mehta Family School of DS and AI IIT Roorkee, India +1