We consider a fairness problem in resource allocation where multiple groups demand resources from a common source with the total fixed amount. The general model was introduced by Elzayn et al. [FAT*19]. We follow Donahue and Kleinberg [FAT*20] who considered the case when the demand distribution is known. We show that for many common demand distributions that satisfy sharp lower tail inequalities, a natural allocation that provides resources proportional to each groups average demand performs very well. More specifically, this natural allocation is approximately fair and efficient (i.e., it provides near maximum utilization). We also show that, when small amount of unfairness is allowed, the Price of Fairness (PoF), in this case, is close to 1.
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