  Existing efforts to formulate computational definitions of fairness have
largely focused on distributional notions of equality, where equality is
defined by the resources or decisions given to individuals in the system. Yet
existing discrimination and injustice is often the result of unequal social
relations, rather than an unequal distribution of resources. Here, we show how
optimizing for existing computational and economic definitions of fairness and
equality fail to prevent unequal social relations. To do this, we provide an
example of a self-confirming equilibrium in a simple hiring market that is
relationally unequal but satisfies existing distributional notions of fairness.
In doing so, we introduce a notion of blatant relational unfairness for
complete-information games, and discuss how this definition helps initiate a
new approach to incorporating relational equality into computational systems.
