On the convergence of multiattribute weighting methods

The convergent validity of ®ve multiattribute weighting methods is studied in an Internet experiment. This is the ®rst experiment where the subjects created the alternatives and attributes themselves. Each subject used ®ve methods to assess attribute weights ± one version of the analytic hierarchy process (AHP), direct point allocation, simple multiattribute rating technique (SMART), swing weighting, and tradeo€ weighting. They can all be used following the principles of multiattribute value theory. Furthermore, SMART, swing, and AHP ask the decision makers to give directly the numerical estimates of weight ratios although the elicitation questions are di€erent. In earlier studies these methods have yielded di€erent weights. Our results suggest that the resulting weights are di€erent because the methods explicitly or implicitly lead the decision makers to choose their responses from a limited set of numbers. The other consequences from this are that the spread of weights and the inconsistency between the preference statements depend on the number of attributes that a decision maker considers simultaneously. Ó 2001 Elsevier Science B.V. All rights reserved.