Classical techniques for cardinal measurement of values, such as direct rating and bisection, are often criticised in decision and psychology literature, because they require from the evaluators the comparison of two pairs of stimuli or alternatives. To bypass this problem, the authors conceived MACBETH (Measuring Attractiveness by a Categorical Based Evaluation Technique), a new approach for the quantification of value judgements, in which the evaluator is asked to give an absolute judgement of difference of attractiveness between two actions. To ease the elaboration of such judgements, a semantic scale of six categories of difference of attractiveness is presented to the evaluator. The numerical scale proposed by MACBETH is obtained by linear programming, so as an indicator of inconsistency of the set of judgements and suggestions to address eventual inconsistency situations. The theoretical problem behind the conception of MACBETH is the one of the numerical representation of multiple semi-orders by constant thresholds. MACBETH is a constructive and interactive approach for decision aid, as illustrated with a real application in public decision making.
