  This paper studies algorithmic fairness when the protected attribute is
location. To handle protected attributes that are continuous, such as age or
income, the standard approach is to discretize the domain into predefined
groups, and compare algorithmic outcomes across groups. However, applying this
idea to location raises concerns of gerrymandering and may introduce
statistical bias. Prior work addresses these concerns but only for regularly
spaced locations, while raising other issues, most notably its inability to
discern regions that are likely to exhibit spatial unfairness. Similar to
established notions of algorithmic fairness, we define spatial fairness as the
statistical independence of outcomes from location. This translates into
requiring that for each region of space, the distribution of outcomes is
identical inside and outside the region. To allow for localized discrepancies
in the distribution of outcomes, we compare how well two competing hypotheses
explain the observed outcomes. The null hypothesis assumes spatial fairness,
while the alternate allows different distributions inside and outside regions.
Their goodness of fit is then assessed by a likelihood ratio test. If there is
no significant difference in how well the two hypotheses explain the observed
outcomes, we conclude that the algorithm is spatially fair.
