Fairness and Utilization in Allocating Resources with Uncertain Demand
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Resource allocation problems are a fundamental domain in which to evaluate the fairness properties of algorithms, and the trade-offs between fairness and utilization have a long history in this domain. A recent line of work has considered fairness questions for resource allocation when the demands for the resource are distributed across multiple groups and drawn from a probability distribution. In such cases, a natural fairness requirement is that individuals from different groups should have (approximately) equal probabilities of receiving the resource. A largely open question in this area has been to bound the gap between the maximum possible utilization of the resource and the maximum subject to this fairness condition. Here we obtain some of the first provable upper bounds on this gap. We show lower bounds but also some general upper bounds for arbitrary distributions, as well as much stronger upper bounds for specific families of distributions that are typically used to model levels of demand. In particular, we find — somewhat surprisingly — that there are natural classes of distributions for which it is possible to simultaneously achieve maximum utilization and the given notion of fairness; and we show that for power-law distributions, there is a non-trivial gap between the solutions, but this gap can be bounded by a constant independent of the parameters of the distribution.
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