A robustness index of binary preferences

Abstract

An index of robustness of the preference between two alternatives is proposed. Given a finite number of alternatives, n conflicting criteria and weights w(i) greater than or equal to 0, i=1,...n representing the preferences of the decision maker, a robustness index r(x,y) is an element of [-1,1] is defined. This index can be seen as a measure of the "robustness" of the preference order of two alternatives x and y with respect to the chosen weights wi, i-1,...n. If r(x,y) is closed to zero, only minor changes of the weights will change the preference order of the alternatives x and y, whereas e.g. a value of r(x,y) close to 1 implies a "strong" preference of x over y. It is shown that the index can also be defined for general additive preference models. A proof that the proposed index, for the additive case, is moderated stochastic transitive is given.