Exponents above one on bounded scores punish weakness more than equal weighting does.

Evidence

Equation (6.3) expresses this through different values of βi. Since all the Di lie in the interval [0, 1], if βi > 1 then this goal is more important, since it reduces the overall evaluation more than dimensions with β = 1: e.g., 0.25 = (0.5)2 < (0.5)1. If Di is a less important factor, then β < 1: e.g., 0.71 = (0.5)0.5 > (0.5)1. In this case the impact of a low Di is mitigated; its impact on the whole is not so severe. If all the βi = 1 then we have equal weights for all parameters and equation (6.3) reduces to equation (6.2). — Gary Goertz, Social Science Concepts and Measurement, 958

Categorization

• CANDY: Because scores sit between zero and one, an exponent larger than one makes a dimension more punishing — counterintuitive to anyone who reads a big exponent as ‘more weight’ in the ordinary sense.