Fairness in Social Influence Maximization via Optimal Transport

TL;DR

This work tackles fairness in influence maximization under stochastic diffusion by introducing mutual fairness, an optimal-transport-based metric that captures the full joint distribution of outreach across two groups. It shows that traditional marginal fairness can misclassify truly unfair outcomes as fair, and derives a closed-form expression for mutual fairness that reduces to the average distance between group outreach proportions. The authors propose S3D, a beta-fairness-aware seed-selection algorithm that optimizes both efficiency and mutual fairness, validated on multiple real networks where fairness improves with minimal or even positive impacts on efficiency. The approach provides a practical framework to certify and improve fairness in information spreading tasks, with implications for health campaigns, marketing, and public policy where equitable reach is critical.

Abstract

We study fairness in social influence maximization, whereby one seeks to select seeds that spread a given information throughout a network, ensuring balanced outreach among different communities (e.g. demographic groups). In the literature, fairness is often quantified in terms of the expected outreach within individual communities. In this paper, we demonstrate that such fairness metrics can be misleading since they overlook the stochastic nature of information diffusion processes. When information diffusion occurs in a probabilistic manner, multiple outreach scenarios can occur. As such, outcomes such as ``In 50% of the cases, no one in group 1 gets the information, while everyone in group 2 does, and in the other 50%, it is the opposite'', which always results in largely unfair outcomes, are classified as fair by a variety of fairness metrics in the literature. We tackle this problem by designing a new fairness metric, mutual fairness, that captures variability in outreach through optimal transport theory. We propose a new seed-selection algorithm that optimizes both outreach and mutual fairness, and we show its efficacy on several real datasets. We find that our algorithm increases fairness with only a minor decrease (and at times, even an increase) in efficiency.

Figures (15)

• Figure 1: Illustration of the ($\gamma_a$,$\gamma_b$) example.
• Figure 2: The transportation cost measures the length of the solid segment; shifts along the diagonal (dotted) are not considered for fairness and are only relevant for efficiency.
• Figure 3: Joint outreach probability distribution for different datasets, different propagation probabilities $p$, and seedsets cardinalities $|S|$.
• Figure 4: Mutual fairness (left, red) and equity (right, blue) for the IV dataset as $p$ varies in $[0,1]$.
• Figure 5: Cost of transporting a point $(x_1,x_2)$ to the "ideal" point $(1,1)$ (i.e., everyone receives the information) for various values of $\beta$ (i.e., we plot $(x_1,x_2)\mapsto c_\beta((x_1,x_2),(1,1))$). Yellow denotes a low transportation cost, whereas dark blue denotes a large cost.

Theorems & Definitions (8)

• Definition 2.1: Final configuration
• Definition 3.1: Mutual Fairness
• Definition 3.2: $\beta$-Fairness
• Definition A.1: Expected outreach ratio
• Definition A.2: Equality AS-AC:19
• Definition A.3: Equity AS-AC:19
• Definition A.4: Max-min fairness GF-BB-MG:20
• Definition A.5: Diversity GF-BB-MG:20