Why the magic number seven plus or minus two

Thomas Saaty
Joseph M. Katz Graduate School of Business
University of Pittsburgh
United States
Mujgan Sagir Ozdemir
Industrial Engineering
Eskisehir Osmangazi University

Publication date: Aug, 2003

Journal: Mathematical and computer modelling
Vol.: 38- Issue: 3-4- Pages: 233-244

Abstract: In 1956, Miller conjectured that there is an upper limit on our capacity to process information on simultaneously interacting elements with reliable accuracy and with validity. This limit is seven plus or minus two elements. He noted that the number 7 occurs in many aspects of life, from the seven wonders of the world to the seven seas and seven deadly sins. We demonstrate in this paper that in making preference judgments on pairs of elements in a group, as we do in the analytic hierarchy process (AHP), the number of elements in the group should be no more than seven. The reason is founded in the consistency of information derived from relations among the elements. When the number of elements increases past seven, the resulting increase in inconsistency is too small for the mind to single out the element that causes the greatest inconsistency to scrutinize and correct its relation to the other elements, and the result is confusion to the mind from the existing information. The AHP as a theory of measurement has a basic way to obtain a measure of inconsistency for any such set of pairwise judgments. When the number of elements is seven or less the inconsistency measurement is relatively large with respect to the number of elements involved; when the number is more it is relatively small. The most inconsistent judgment is easily determined in the first case and the individual providing the judgments can change it in an effort to improve the overall inconsistency. In the second case, as the inconsistency measurement is relatively small, improving inconsistency requires only small perturbations and the judge would be hard put to determine what that change should be, and how such a small change could be justified for improving the validity of the outcome. The mind is sufficiently sensitive to improve large inconsistencies but not small ones. And the implication of this is that the number of elements in a set should be limited to seven plus or minus two.

Keywords: Pairwise comparison, Consistency, Decision making, Analytic Hierarchy Process, AHP