  Consequential decision-making incentivizes individuals to strategically adapt
their behavior to the specifics of the decision rule. While a long line of work
has viewed strategic adaptation as gaming and attempted to mitigate its
effects, recent work has instead sought to design classifiers that incentivize
individuals to improve a desired quality. Key to both accounts is a cost
function that dictates which adaptations are rational to undertake. In this
work, we develop a causal framework for strategic adaptation. Our causal
perspective clearly distinguishes between gaming and improvement and reveals an
important obstacle to incentive design. We prove any procedure for designing
classifiers that incentivize improvement must inevitably solve a non-trivial
causal inference problem. Moreover, we show a similar result holds for
designing cost functions that satisfy the requirements of previous work. With
the benefit of hindsight, our results show much of the prior work on strategic
classification is causal modeling in disguise.
