The study of influence maximization in social networks has largely ignored disparate effects these algorithms might have on the individuals contained in the social network. Individuals may place a high value on receiving information, e.g. job openings or advertisements for loans. While well-connected individuals at the center of the network are likely to receive the information that is being distributed through the network, poorly connected individuals are systematically less likely to receive the information, producing a gap in access to the information between individuals. In this work, we study how best to spread information in a social network while minimizing this access gap.
We propose to use the maximin social welfare function as an objective function, where we maximize the minimum probability of receiving the information under an intervention. We prove that in this setting this welfare function constrains the access gap whereas maximizing the expected number of nodes reached does not. We also investigate the difficulties of using the maximin, and present hardness results and analysis for standard greedy strategies. Finally, we investigate practical ways of optimizing for the maximin, and give empirical evidence that a simple greedy-based strategy works well in practice.
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Pipeline Interventions
We introduce the \emph{pipeline intervention} problem, defined by a layered directed acyclic graph and a set of stochastic matrices governing transitions between successive layers. The graph is a stylized model for how people from different populations are presented opportunities, eventually leading to some reward. In our model, individuals are born into an initial position (i.e. some node in the first layer of the graph) according to a fixed probability distribution, and then stochastically progress through the graph according to the transition matrices, until they reach a node in the final layer of the graph; each node in the final layer has a \emph{reward} associated with it. The pipeline intervention problem asks how to best make costly changes to the transition matrices governing people's stochastic transitions through the graph, subject to a budget constraint. We consider two objectives: social welfare maximization, and a fairness-motivated maximin objective that seeks to maximize the value to the population (starting node) with the \emph{least} expected value. We consider two variants of the maximin objective that turn out to be distinct, depending on whether we demand a deterministic solution or allow randomization. For each objective, we give an efficient approximation algorithm (an additive FPTAS) for constant width networks. We also tightly characterize the "price of fairness" in our setting: the ratio between the highest achievable social welfare and the highest social welfare consistent with a maximin optimal solution. Finally we show that for polynomial width networks, even approximating the maximin objective to any constant factor is NP hard, even for networks with constant depth. This shows that the restriction on the width in our positive results is essential.
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- Award ID(s):
- 1763307
- NSF-PAR ID:
- 10267300
- Date Published:
- Journal Name:
- 12th Innovations in Theoretical Computer Science Conference (ITCS 2021)
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.4230/LIPIcs.ITCS.2021.8
