  Deploying an algorithmically informed policy is a significant intervention in
society. Prominent methods for algorithmic fairness focus on the distribution
of predictions at the time of training, rather than the distribution of social
goods that arises after deploying the algorithm in a specific social context.
However, requiring a "fair" distribution of predictions may undermine efforts
at establishing a fair distribution of social goods. First, we argue that
addressing this problem requires a notion of prospective fairness that
anticipates the change in the distribution of social goods after deployment.
Second, we provide formal conditions under which this change is identified from
pre-deployment data. That requires accounting for different kinds of
performative effects. Here, we focus on the way predictions change policy
decisions and, consequently, the causally downstream distribution of social
goods. Throughout, we are guided by an application from public administration:
the use of algorithms to predict who among the recently unemployed will remain
unemployed in the long term and to target them with labor market programs.
Third, using administrative data from the Swiss public employment service, we
simulate how such algorithmically informed policies would affect gender
inequalities in long-term unemployment. When risk predictions are required to
be "fair" according to statistical parity and equality of opportunity,
targeting decisions are less effective, undermining efforts to both lower
overall levels of long-term unemployment and to close the gender gap in
long-term unemployment.
