We study fairness in social influence maximization, whereby one seeks to selectseeds that spread a given information throughout a network, ensuring balancedoutreach among different communities (e.g. demographic groups). In the literature,fairness is often quantified in terms of the expected outreach within individualcommunities. In this paper, we demonstrate that such fairness metrics can bemisleading since they overlook the stochastic nature of information diffusionprocesses. When information diffusion occurs in a probabilistic manner, multipleoutreach scenarios can occur. As such, outcomes such as “In 50% of the cases, noone in group 1 gets the information, while everyone in group 2 does, and in theother 50%, it is the opposite”, which always results in largely unfair outcomes,are classified as fair by a variety of fairness metrics in the literature. We tacklethis problem by designing a new fairness metric, mutual fairness, that capturesvariability in outreach through optimal transport theory. We propose a new seed-selection algorithm that optimizes both outreach and mutual fairness, and we showits efficacy on several real datasets. We find that our algorithm increases fairnesswith only a minor decrease (and at times, even an increase) in efficiency.