  There is a lack of consensus within the literature as to how `fairness' of
algorithmic systems can be measured, and different metrics can often be at
odds. In this paper, we approach this task by drawing on the ethical frameworks
of utilitarianism and John Rawls. Informally, these two theories of
distributive justice measure the `good' as either a population's sum of
utility, or worst-off outcomes, respectively. We present a parameterized class
of objective functions that interpolates between these two (possibly)
conflicting notions of the `good'. This class is shown to represent a
relaxation of the Rawlsian `veil of ignorance', and its sequence of optimal
solutions converges to both a utilitarian and Rawlsian optimum. Several other
properties of this class are studied, including: 1) a relationship to
regularized optimization, 2) feasibility of consistent estimation, and 3)
algorithmic cost. In several real-world datasets, we compute optimal solutions
and construct the tradeoff between utilitarian and Rawlsian notions of the
`good'. Empirically, we demonstrate that increasing model complexity can
manifest strict improvements to both measures of the `good'. This work suggests
that the proper degree of `fairness' can be informed by a designer's
preferences over the space of induced utilitarian and Rawlsian `good'.
