Fairness-aware design of nudging policies under stochasticity and prejudices

We present an injustice-aware innovation-diffusion model extending the Generalized Linear Threshold framework by assigning agents activation thresholds drawn from a Beta distribution to capture the stochastic nature of adoption shaped by inequalities. Because incentive policies themselves can inadvertently amplify these inequalities, building on this model, we design a fair Model Predictive Control (MPC) scheme that incorporates equality and equity objectives for allocating incentives. Simulations using real mobility-habit data show that injustice reduces overall adoption, while equality smooths incentive distribution and equity reduces disparities in the final outcomes. Thus, incorporating fairness ensures effective diffusion without exacerbating existing social inequalities.

💡 Research Summary

The paper tackles the problem of designing nudging policies for technology adoption that are both effective and fair, taking into account stochastic decision making and epistemic injustices. Building on the Generalized Linear Threshold (GLT) model, the authors introduce a stochastic reformulation where each agent’s adoption threshold is drawn from a Beta distribution whose parameters depend on the agent’s current “reluctance” (ρ). This captures the inherent uncertainty in individual adoption decisions: agents with high reluctance require a larger fraction of adopting neighbors to switch, while agents with low reluctance need only a small influence. The expected value of the Beta‑distributed threshold equals ρ, preserving the deterministic model’s intuition while adding probabilistic richness.

To model epistemic bias, each agent is endowed with two additional attributes: actual competence (ζ) and perceived credibility (γ). The gap Δ = ζ − γ quantifies a credibility deficit caused by social prejudice (e.g., gender, race, or class). The influence weight θ_v used in the threshold condition is modified to sum the credibility‑weighted adoption states of neighbors, so that agents perceived as less credible exert weaker influence regardless of their true competence. This mechanism embeds epistemic injustice directly into the diffusion dynamics.

The authors then formulate a fairness‑aware Model Predictive Control (MPC) problem. Two fairness dimensions are considered: (i) equality, which penalizes uneven distribution of incentives u_v(t) across the population, and (ii) equity, which seeks to minimize disparities in final adoption rates among predefined social groups. The MPC objective combines (a) maximization of total adoption, (b) minimization of total incentive expenditure, (c) reduction of inter‑group adoption variance, and (d) adherence to a budget constraint. At each time step, the current network state and the stochastic diffusion model are used to predict future states; an optimization yields the incentive vector for the next step, which is then applied before the process repeats.

Empirical evaluation uses an EU‑wide mobility‑habits survey to construct a realistic social network and seed set of early adopters. Three policy scenarios are compared: (1) a baseline with no fairness constraints, (2) an equality‑focused policy, and (3) an equity‑focused policy. Results show that when epistemic injustice is present (γ ≪ ζ for disadvantaged groups), overall adoption drops and adoption concentrates among high‑credibility, high‑income agents. The equality‑only policy smooths incentive allocation but does not significantly boost adoption. In contrast, the equity‑oriented policy maintains high overall adoption while markedly reducing group‑level adoption gaps. Thus, incorporating fairness leads to both efficient diffusion and a more socially balanced outcome.

Key contributions are: (1) a stochastic GLT model with Beta‑distributed thresholds linked to agent reluctance, (2) a novel representation of epistemic bias via credibility weights, (3) a unified MPC framework that simultaneously optimizes equality and equity, and (4) a data‑driven simulation demonstrating the practical benefits of fairness‑aware nudging. The paper suggests future extensions such as relaxing the irreversible‑adoption assumption, handling multiple concurrent innovations, and integrating real‑time data streams for adaptive control.