  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 ignore 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 of group 1 receives the information and
everyone in group 2 receives it and in other 50%, the opposite happens", 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.
