LINEAR COMPOSITES IN MULTIATTRIBUTE JUDGMENT AND CHOICE - EXTENSIONS OF WILKS RESULTS TO ZERO AND NEGATIVELY CORRELATED ATTRIBUTES

One of the most common ways of evaluating two or more options that var y along multiple criteria is to form linear composites that incorporat e the decision maker's assessment of the relative importance of each c riterion. Variations of this procedure are prevalent in both the behav ioural and policy disciplines. Over 50 years ago Wilks (1938) showed t hat if the criteria underlying the options are sufficiently highly cor related then the choice of weights does not matter, in the sense that the correlation between composites formed from any two independent set s of ratings tends to 1 as the number of criteria increases. Wilks' re sult, however, requires two assumptions, namely positively correlated attributes and independent choices of weights. Through various extensi ons of his results, we show that Wilks' conclusion is highly robust-on ly extreme, simultaneous violation of both assumptions produces negati vely correlated composites.