  Fairness of exposure is a commonly used notion of fairness for ranking
systems. It is based on the idea that all items or item groups should get
exposure proportional to the merit of the item or the collective merit of the
items in the group. Often, stochastic ranking policies are used to ensure
fairness of exposure. Previous work unrealistically assumes that we can
reliably estimate the expected exposure for all items in each ranking produced
by the stochastic policy. In this work, we discuss how to approach fairness of
exposure in cases where the policy contains rankings of which, due to
inter-item dependencies, we cannot reliably estimate the exposure distribution.
In such cases, we cannot determine whether the policy can be considered fair.
Our contributions in this paper are twofold. First, we define a method called
FELIX for finding stochastic policies that avoid showing rankings with unknown
exposure distribution to the user without having to compromise user utility or
item fairness. Second, we extend the study of fairness of exposure to the top-k
setting and also assess FELIX in this setting. We find that FELIX can
significantly reduce the number of rankings with unknown exposure distribution
without a drop in user utility or fairness compared to existing fair ranking
methods, both for full-length and top-k rankings. This is an important first
step in developing fair ranking methods for cases where we have incomplete
knowledge about the user's behaviour.
