  Motivated by a plethora of practical examples where bias is induced by
automated-decision making algorithms, there has been strong recent interest in
the design of fair algorithms. However, there is often a dichotomy between
fairness and efficacy: fair algorithms may proffer low social welfare solutions
whereas welfare optimizing algorithms may be very unfair. This issue is
exemplified in the machine scheduling problem where, for $n$ jobs, the social
welfare of any fair solution may be a factor $\Omega(n)$ worse than the optimal
welfare. In this paper, we prove that this dichotomy between fairness and
efficacy can be overcome if we allow for a negligible amount of bias: there
exist algorithms that are both "almost perfectly fair" and have a constant
factor efficacy ratio, that is, are guaranteed to output solutions that have
social welfare within a constant factor of optimal welfare. Specifically, for
any $\epsilon>0$, there exist mechanisms with efficacy ratio
$\Theta(\frac{1}{\epsilon})$ and where no agent is more than an $\epsilon$
fraction worse off than they are in the fairest possible solution (given by an
algorithm that does not use personal or type data). Moreover, these bicriteria
guarantees are tight and apply to both the single machine case and the multiple
machine case. The key to our results are the use of Pareto scheduling
mechanisms. These mechanisms, by the judicious use of personal or type data,
are able to exploit Pareto improvements that benefit every individual; such
Pareto improvements would typically be forbidden by fair scheduling algorithms
designed to satisfy standard statistical measures of group fairness. We
anticipate this paradigm, the judicious use of personal data by a fair
algorithm to greatly improve performance at the cost of negligible bias, has
wider application.
