A note on the indeterminacy and arbitrariness of pena’s method of construction of synthetic indicators

In this paper we demonstrate that Pena’s method of construction of a synthetic indicator is very sensitive to the order in which the constituent variables (whose linear aggregation yields the synthetic indicator) are arranged. Since m number of constituent variables may be arranged in m-factorial ways, even a moderately large m can give rise to a very large number of synthetic indicators from which one cannot choose the one which best represents the constituent variables. Given that an analyst has too little information as to the order in which a sizeable number of constituent variables must be arranged so as to obtain the best representative synthetic indicator, Pena’s method can give only an arbitrary synthetic indicator whose representativeness is indeterminate and uncertain.