International Encyclopedia of Systems and Cybernetics

T.R. BURNS and L.D. MEEKER draw our attention on a very subtle invisible conceptual trap, which is the implicit belief in transitivity which pervades much of our toughts:

"Intransitivities in Multi-Criteria Evaluation and Decision-Making

"A property of evaluation and decision orderings which has been of considerable importance in decision-making research and theory is that of transitivity: x preferred to y and y preferred to z and (thus) x preferred to z.

"Intransitivities, or cycles, e.g. x preferred to y, y preferred to z and z preferred to x, either have been ruled out, certainly in the case of "rational decision-makers", or have presented a serious challenge to the classical decision and games models with their assumptions of uni-dimensionality (ordinal or cardinal utility scales) and consistency" (1976, p.115).

From their theoretical perspective, these authors consider that "… intransitivities are inherent in multi-criteria evaluation and decision-making. Fluctuations in the criteria used or in the relative importance of multiple criteria with respect to different sub-sets of items typically leads to violations of transitivity" (Ibid).