  Liberalism-oriented political philosophy reasons that all individuals should
be treated equally independently of their protected characteristics. Related
work in machine learning has translated the concept of \emph{equal treatment}
into terms of \emph{equal outcome} and measured it as \emph{demographic parity}
(also called \emph{statistical parity}). Our analysis reveals that the two
concepts of equal outcome and equal treatment diverge; therefore, demographic
parity does not faithfully represent the notion of \emph{equal treatment}. We
propose a new formalization for equal treatment by (i) considering the
influence of feature values on predictions, such as computed by Shapley values
decomposing predictions across its features, (ii) defining distributions of
explanations, and (iii) comparing explanation distributions between populations
with different protected characteristics. We show the theoretical properties of
our notion of equal treatment and devise a classifier two-sample test based on
the AUC of an equal treatment inspector. We study our formalization of equal
treatment on synthetic and natural data. We release \texttt{explanationspace},
an open-source Python package with methods and tutorials.
