THERE has been a controversy of long standing in industrial psychology between the advocates of the single composite criterion and those favoring multiple criteria. Earlier writers on this problem tended to favor the composite criterion concept (Toops, 1944;Brogden and Taylor, 1950; Nagel, 1953), and this doctrine remained essentially unchallenged until the second half of the fifties. Then, starting in 1956, a series of statements by a number of wellknown industrial psychologists appeared seriously questioning the utility of this concept and concluded that, in most cases, the use of multiple criteria was to be preferred to the use of the traditional composite (Ghiselli, 1956; Guion, 1961Guion, , 1965 Dunnette, 1963a Dunnette, , 1963b. To date, this controversy has not been satisfactorily resolved, as is obvious from the cautious and rather indecisive treatment the question receives in most standard texts in industrial psychology (Tiffin and McCormick, 1965, pp. 47-54, Blum and Naylor, 1968, pp. 184-193). The purpose of this paper is to set forth the basic arguments advanced for each position, to explore the assumptions underlying these arguments, and, finally, to offer a practical and conceptual resolution of the controversy.