  We consider a selection problem where sequentially arrived applicants apply
for a limited number of positions/jobs. At each time step, a decision maker
accepts or rejects the given applicant using a pre-trained supervised learning
model until all the vacant positions are filled. In this paper, we discuss
whether the fairness notions (e.g., equal opportunity, statistical parity,
etc.) that are commonly used in classification problems are suitable for the
sequential selection problems. In particular, we show that even with a
pre-trained model that satisfies the common fairness notions, the selection
outcomes may still be biased against certain demographic groups. This
observation implies that the fairness notions used in classification problems
are not suitable for a selection problem where the applicants compete for a
limited number of positions. We introduce a new fairness notion, ``Equal
Selection (ES),'' suitable for sequential selection problems and propose a
post-processing approach to satisfy the ES fairness notion. We also consider a
setting where the applicants have privacy concerns, and the decision maker only
has access to the noisy version of sensitive attributes. In this setting, we
can show that the perfect ES fairness can still be attained under certain
conditions.
