A Note on the Sub-Optimality of Rank Ordering of Objects on the Basis of the Leading Principal Component Factor Scores

Abstract:     
This paper demonstrates that if we intend to optimally rank order n objects (candidates) each of which has m rank-ordered attributes or rank scores awarded by m evaluators, then the overall ordinal ranking of objects by the conventional principal component based factor scores turns out to be suboptimal. Three numerical examples have been provided to show that principal component based rankings do not necessarily maximize the sum of squared correlation coefficients between the individual m rank scores arrays, X(n,m), and overall rank scores array, Z(n).

Keywords: Rankings, sub-optimal, optimality, principal component, factor scores, Differential Evolution, global optimization

JEL Classifications: C13, C43, C61, C87, C88

Working Paper Series