Though I don't know when the quota/total system began, I know was in place in the late 1960's.
It's interesting to look through old college yearbooks (many of them have been digitized and can be found via university websites either as part of their libraries or their archives) and see the variation in size among the sororities on one campus. One might have a pledge class of five one year and ten the next, and vice versa for the group next door. (And in those olden days the yearbooks often listed a GLO's entire chapter roll, and "sorors in facultate (sp)" and "sorors in urbe (sp)" -- that is, the alumnae on the faculty and in town -- as well as the undergraduate members.)
From
www.npcwomen.org:
"Early histories of women's fraternities contain accounts of "rushing and pledging agreements" or "compacts" among fraternities on various campuses, and also many stories of cooperation and mutual assistance. However, no actual Panhellenic organization existed and no uniform practices were observed. By 1902, it was obvious that some standards were needed, so Alpha Phi invited Pi Beta Phi, Kappa Alpha Theta, Kappa Kappa Gamma, Delta Gamma, Gamma Phi Beta, Delta Delta Delta, Alpha Chi Omega and Chi Omega to a conference in Chicago on May 24. Alpha Chi Omega and Chi Omega were unable to attend. The remaining seven groups met and the session resulted in the organization of the first interfraternity association and the first intergroup organization on college campuses. (National Interfraternity Conference for men's fraternities was organized in 1909, now called the North-American Interfraternity Conference).
"This meeting, and the next few, resulted in several mutual agreements, especially regarding pledging.
Up to this time, no guidelines had been set, and women could be pledged to groups before enrolling in college and, indeed, even belong to more than one group." [emphasis added]