  Several behavioral, social, and public health interventions, such as
suicide/HIV prevention or community preparedness against natural disasters,
leverage social network information to maximize outreach. Algorithmic influence
maximization techniques have been proposed to aid with the choice of "peer
leaders" or "influencers" in such interventions. Yet, traditional algorithms
for influence maximization have not been designed with these interventions in
mind. As a result, they may disproportionately exclude minority communities
from the benefits of the intervention. This has motivated research on fair
influence maximization. Existing techniques come with two major drawbacks.
First, they require committing to a single fairness measure. Second, these
measures are typically imposed as strict constraints leading to undesirable
properties such as wastage of resources.
  To address these shortcomings, we provide a principled characterization of
the properties that a fair influence maximization algorithm should satisfy. In
particular, we propose a framework based on social welfare theory, wherein the
cardinal utilities derived by each community are aggregated using the
isoelastic social welfare functions. Under this framework, the trade-off
between fairness and efficiency can be controlled by a single inequality
aversion design parameter. We then show under what circumstances our proposed
principles can be satisfied by a welfare function. The resulting optimization
problem is monotone and submodular and can be solved efficiently with
optimality guarantees. Our framework encompasses as special cases leximin and
proportional fairness. Extensive experiments on synthetic and real world
datasets including a case study on landslide risk management demonstrate the
efficacy of the proposed framework.
