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Linear composites in multiattribute judgement and choice: Extensions of Wilks' results to zero and negatively correlated attributes
Author(s) -
Krieger Abba M.,
Green Paul E.
Publication year - 1996
Publication title -
british journal of mathematical and statistical psychology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.157
H-Index - 51
eISSN - 2044-8317
pISSN - 0007-1102
DOI - 10.1111/j.2044-8317.1996.tb01077.x
Subject(s) - judgement , mathematics , decision maker , zero (linguistics) , linear correlation , correlation , econometrics , statistics , operations research , epistemology , philosophy , geometry , linguistics
One of the most common ways of evaluating two or more options that vary along multiple criteria is to form linear composites that incorporate the decision maker's assessment of the relative importance of each criterion. Variations of this procedure are prevalent in both the behavioural and policy disciplines. Over 50 years ago Wilks (1 938) showed that if the criteria underlying the options are sufficiently highly correlated then the choice of weights does not matter, in the sense that the correlation between composites formed from any two independent sets of ratings tends to 1 as the number of criteria increases. Wilks' result, however, requires two assumptions, namely positively correlated attributes and independent choices of weights. Through various extensions of his results, we show that Wilks' conclusion is highly robust‐nly extreme, simultaneous violation of both assumptions produces negatively correlated composites.