An allocation rule

A town has 100 study-room hours to divide between neighbourhoods East and West. East has 100 applicants and West has 50. A survey estimates that East applicants have 200 hours of adequate private study space in total each week; West applicants have none. The following options are under discussion: Plan P: East 50 room-hours; West 50 room-hours. Plan Q: East 67 room-hours; West 33 room-hours. Plan R: East 25 room-hours; West 75 room-hours. One applicant uses one room for one hour; all allocated hours will be used. Fractions arising from per-applicant averages need not correspond to an individual booking. Councillor Vale calls P “equal treatment”. Councillor Noor favours R because “a public hour can matter more where private alternatives are absent”. Councillor Ellis favours Q because “each applicant should have approximately the same claim on the new service”. The survey does not show how East's private hours are distributed among its applicants. The chair says that the figures make the disagreement precise, but do not by themselves resolve it.