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Perceived Fairness in Networks

Arthur Charpentier

TL;DR

This work distinguishes objective fairness from perceived fairness by embedding decisions in a network and formalizing local fairness perception via a $d$-hop neighbor comparison. It proves that, although global demographic parity can hold, local perceptions may diverge due to topology, with convergence to global fairness as $d\to\infty$ on connected graphs and amplification of perceived discrimination under homophily or assortative mixing. The authors derive linear-response results under a two-block SBM, bound the perception gap with modularity, and show clustering can stabilize perceptions, supplemented by numerical SBM simulations. The framework provides a quantitative bridge between network structure and social experience, with implications for governance, policy, and applications in finance and decentralized systems where outcomes are partially observed through peers.

Abstract

The usual definitions of algorithmic fairness focus on population-level statistics, such as demographic parity or equal opportunity. However, in many social or economic contexts, fairness is not perceived globally, but locally, through an individual's peer network and comparisons. We propose a theoretical model of perceived fairness networks, in which each individual's sense of discrimination depends on the local topology of interactions. We show that even if a decision rule satisfies standard criteria of fairness, perceived discrimination can persist or even increase in the presence of homophily or assortative mixing. We propose a formalism for the concept of fairness perception, linking network structure, local observation, and social perception. Analytical and simulation results highlight how network topology affects the divergence between objective fairness and perceived fairness, with implications for algorithmic governance and applications in finance and collaborative insurance.

Perceived Fairness in Networks

TL;DR

This work distinguishes objective fairness from perceived fairness by embedding decisions in a network and formalizing local fairness perception via a -hop neighbor comparison. It proves that, although global demographic parity can hold, local perceptions may diverge due to topology, with convergence to global fairness as on connected graphs and amplification of perceived discrimination under homophily or assortative mixing. The authors derive linear-response results under a two-block SBM, bound the perception gap with modularity, and show clustering can stabilize perceptions, supplemented by numerical SBM simulations. The framework provides a quantitative bridge between network structure and social experience, with implications for governance, policy, and applications in finance and decentralized systems where outcomes are partially observed through peers.

Abstract

The usual definitions of algorithmic fairness focus on population-level statistics, such as demographic parity or equal opportunity. However, in many social or economic contexts, fairness is not perceived globally, but locally, through an individual's peer network and comparisons. We propose a theoretical model of perceived fairness networks, in which each individual's sense of discrimination depends on the local topology of interactions. We show that even if a decision rule satisfies standard criteria of fairness, perceived discrimination can persist or even increase in the presence of homophily or assortative mixing. We propose a formalism for the concept of fairness perception, linking network structure, local observation, and social perception. Analytical and simulation results highlight how network topology affects the divergence between objective fairness and perceived fairness, with implications for algorithmic governance and applications in finance and collaborative insurance.

Paper Structure

This paper contains 28 sections, 9 theorems, 44 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Related Work
  3. Group and Individual Fairness
  4. Network Topology and Distortions
  5. Perceived Discrimination and Social Psychology
  6. Model of Perceived Fairness
  7. Setup and notation
  8. Objective (global) fairness.
  9. Local observation and fairness perception
  10. Fairness perception.
  11. Two exposure operators and edge weighting
  12. Asymptotics in neighborhood radius
  13. Assortative networks and homophily
  14. Perceived fairness gap under DP
  15. Bounds via modularity
  16. ...and 13 more sections

Key Result

Proposition 3.1

Suppose $G$ is connected and $h$ is non-degenerate (both acceptance and rejection occur with positive probability in each group). Then for each $s\in\{A,B\}$, and hence, if DP eq:DP holds, $\lim_{d\to\infty}\Delta_d(h)=0$.

Figures (1)

  • Figure 1: Relationship between network homophily and perceived fairness gap. Each point represents the average over repeated stochastic block–model simulations with varying within-group connectivity. While the global fairness gap (difference in mean outcomes between groups) remains nearly constant, the perceived fairness gap—computed from local comparisons with neighbors—grows approximately linearly with the homophily index. This illustrates how assortative mixing amplifies subjective perceptions of discrimination, even when global fairness holds.

Theorems & Definitions (19)

  • Proposition 3.1: Perception convergence
  • proof : Proof sketch
  • Theorem 3.1: Small-radius perceived gap under DP
  • proof : Proof of Theorem \ref{['thm:gap']} (linear response under SBM)
  • Remark 3.1: DP edge case
  • Remark 3.2: Degree exposure and linear effect under DP
  • Corollary 3.1: Sign and monotonicity
  • Proposition 3.2: Perception gap and assortativity
  • proof : Proof idea
  • Proposition 3.3: Topology smoothing reduces dispersion
  • ...and 9 more