  Existing fair ranking systems, especially those designed to be
demographically fair, assume that accurate demographic information about
individuals is available to the ranking algorithm. In practice, however, this
assumption may not hold -- in real-world contexts like ranking job applicants
or credit seekers, social and legal barriers may prevent algorithm operators
from collecting peoples' demographic information. In these cases, algorithm
operators may attempt to infer peoples' demographics and then supply these
inferences as inputs to the ranking algorithm.
  In this study, we investigate how uncertainty and errors in demographic
inference impact the fairness offered by fair ranking algorithms. Using
simulations and three case studies with real datasets, we show how demographic
inferences drawn from real systems can lead to unfair rankings. Our results
suggest that developers should not use inferred demographic data as input to
fair ranking algorithms, unless the inferences are extremely accurate.
