Abstract
The rise of algorithmic decision making led to active researches on how to define and guarantee fairness, mostly focusing on one-shot decision making. In several important applications such as hiring, however, decisions are made in multiple stage
with additional information at each stage. In such
cases, fairness issues remain poorly understood.
In this paper we study fairness in k-stage selection
problems where additional features are observed at
every stage. We first introduce two fairness notions, local (per stage) and global (final stage) fairness, that extend the classical fairness notions to
the k-stage setting. We propose a simple model
based on a probabilistic formulation and show that
the locally and globally fair selections that maximize precision can be computed via a linear program. We then define the price of local fairness
to measure the loss of precision induced by local
constraints; and investigate theoretically and empirically this quantity. In particular, our experiments
show that the price of local fairness is generally
smaller when the sensitive attribute is observed at
the first stage; but globally fair selections are more
locally fair when the sensitive attribute is observed
at the second stage—hence in both cases it is often
possible to have a selection that has a small price of
local fairness and is close to locally fair.