Fair Influence Maximization: A Welfare Optimization Approach

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.Comment: The short version of this paper appears in the proceedings of AAAI-2

Simplification and Improvement of MMS Approximation

We consider the problem of fairly allocating a set of indivisible goods among $n$ agents with additive valuations, using the popular fairness notion of maximin share (MMS). Since MMS allocations do not always exist, a series of works provided existence and algorithms for approximate MMS allocations. The current best approximation factor, for which the existence is known, is $(\frac{3}{4} + \frac{1}{12n})$ [Garg and Taki, 2021]. Most of these results are based on complicated analyses, especially those providing better than $2/3$ factor. Moreover, since no tight example is known of the Garg-Taki algorithm, it is unclear if this is the best factor of this approach. In this paper, we significantly simplify the analysis of this algorithm and also improve the existence guarantee to a factor of $(\frac{3}{4} + \min(\frac{1}{36}, \frac{3}{16n-4}))$. For small $n$, this provides a noticeable improvement. Furthermore, we present a tight example of this algorithm, showing that this may be the best factor one can hope for with the current techniques