You need to operationalize "quality". Quality in this context simply means "goodness", which is subjective. If by quality you mean "leads to life success", then prestige seem to be a good proxy for "quality" (though the selection effect makes it less clear).

For example, going to Harvard Business school might lead to life success due to possible employers wanting to affiliate with your high status associations, even if the education leads to lower productivity gains than community college business courses and a few years of employment in the field.