Fair Influence Maximization: A Welfare Optimization Approach
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Several social interventions (e.g., suicide and HIV prevention) leverage social network information to maximize outreach. Algorithmic influence maximization techniques have been proposed to aid with the choice of influencers (or peer leaders) in such interventions. Traditional algorithms for influence maximization have not been designed with social 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 require committing to a single domain-specific fairness measure. This makes it hard for a decision maker to meaningfully compare these notions and their resulting trade-offs across different applications. We address these shortcomings by extending the principles of cardinal welfare to the influence maximization setting, which is underlain by complex connections between members of different communities. We generalize the theory regarding these principles and show under what circumstances these principles can be satisfied by a welfare function. We then propose a family of welfare functions that are governed by a single inequity aversion parameter which allows a decision maker to study task-dependent trade-offs between fairness and total influence and effectively trade off quantities like influence gap by varying this parameter. We use these welfare functions as a fairness notion to rule out undesirable allocations. We show that the resulting optimization problem is monotone and submodular and can be solved with optimality guarantees. Finally, we carry out a detailed experimental analysis on synthetic and real social networks and should that high welfare can be achieved without sacrificing the total influence significantly. Interestingly we can show there exists welfare functions that empirically satisfy all of the principles.
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