  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 group's 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.
