The task of setting punitive damages most closely resembles a particular psychophysical
method, which we have labeled magnitude scaling without a modulus. As was noted
earlier, subjects in most applications of magnitude scaling are instructed to assign a
particular number (the modulus) to a specified standard stimulus, and to judge other
stimuli in terms of ratios of subjective intensity relative to that standard. The modulus is
both arbitrary and inconsequential: the same ratio scales will be obtained regardless of
whether the standard stimulus is to be judged 10 or 100. However, magnitude scaling can
also be conducted without a modulus, by instructing subjects to ensure that their judgments
of different stimuli should reflect the ratios of the intensity of subjective experience.
In the context of psychophysical scaling (e.g., of loudness), the procedure yields scales
that are quite similar to those that are obtained in the standard method, though somewhat
noisier and more skewed. It appears that a subject in such an experiment spontaneously
adopts a modulus—and different subjects adopt different moduli. Naturally, this procedure
greatly increases the variability and skewness of the numerical responses to any given
stimulus. The effects of individual differences in the size of the modulus are easily
eliminated in the statistical analysis of psychophysical data, where each observer judges
many stimuli. Under current legal practice, this remedy is not available, since each jury
considers only one case in isolation, and indeed is explicitly prohibited from comparing
it to others.