Women could not participate, so it was definitely more cut-throat than Harvard for half the population. The article gives a figure of ~1M taking the provincial

Women could not participate, so it was definitely more cut-throat than Harvard for half the population. The article gives a figure of ~1M taking the provincial exam annually during the Ming dynasty, with the later Ming empire having a population in the range 160-200M. You are probably right about self-selection being greater for Harvard, then, given that just about anyone can, in principle, apply there.