  Prediction models have been widely adopted as the basis for decision-making
in domains as diverse as employment, education, lending, and health. Yet, few
real world problems readily present themselves as precisely formulated
prediction tasks. In particular, there are often many reasonable target
variable options. Prior work has argued that this is an important and sometimes
underappreciated choice, and has also shown that target choice can have a
significant impact on the fairness of the resulting model. However, the
existing literature does not offer a formal framework for characterizing the
extent to which target choice matters in a particular task. Our work fills this
gap by drawing connections between the problem of target choice and recent work
on predictive multiplicity. Specifically, we introduce a conceptual and
computational framework for assessing how the choice of target affects
individuals' outcomes and selection rate disparities across groups. We call
this multi-target multiplicity. Along the way, we refine the study of
single-target multiplicity by introducing notions of multiplicity that respect
resource constraints -- a feature of many real-world tasks that is not captured
by existing notions of predictive multiplicity. We apply our methods on a
healthcare dataset, and show that the level of multiplicity that stems from
target variable choice can be greater than that stemming from nearly-optimal
models of a single target.
