We study fairness in social influence maximization, whereby one seeks to select seeds that spread a given information throughout a network, ensuring balanced outreach among different communities (e.g. demographic groups). In the literature, fairness is often quantified in terms of the expected outreach within individual communities. In this paper, we demonstrate that such fairness metrics can be misleading since they overlook the stochastic nature of information diffusion processes. When information diffusion occurs in a probabilistic manner, multiple outreach scenarios can occur. As such, outcomes such as “In 50% of the cases, no one in group 1 gets the information, while everyone in group 2 does, and in the other 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 tackle this problem by designing a new fairness metric, mutual fairness, that captures variability in outreach through optimal transport theory. We propose a new seed- selection algorithm that optimizes both outreach and mutual fairness, and we show its efficacy on several real datasets. We find that our algorithm increases fairness with only a minor decrease (and at times, even an increase) in efficiency.