Suppose we have a population of individuals on each of which we have measures of p different traits, the measures being xi, i = 1, 2, ..., p. The problem is considered of selecting the best individuals with respect to all p traits combined when nothing is to be assumed about what economic weights are appropriate. One recommended index for selection is P[PI] (xi-ki), where ki is the smallest value of xi occurring in the population. This index is intuitively appealing in that it satisfies what economists call the "law of substitution"; it has a certain invariance property; and, if the distributions of xi-ki differ for different i by scale factors only, then this index is equivalent to the sum of the p measures as taken on a scale on which they are equally variable. Further invariance is gained by using the index P[PI] (xi[image]-ki[image]), where xi[image] = log (xi-ki) and ki[image] i=1 is the smallest value of log (xi-ki). Methods are given for modifying these indices to enable ranking of all individuals and to allow for errors of measurement. Their use is illustrated for two traits measured on chickens.