This paper posits a classification of tertiary education institutions into four tiers: world research universities, selecting universities, recruiting universities, and vocational institutes. The distinguishing characteristic of world research universities is their research strength, the distinguishing characteristic of selecting universities is their strong student demand, the distinguishing characteristic of recruiting universities is their lower student demand, and the distinguishing characteristic of vocational institutes is their predominance of vocational programs. Yet there is one general characteristic that underlies the whole classification: positional value. The classification is put within a theoretical framework which generates tests of the classification proposed in the paper.