If magnitude estimates are definitive measures of sensation, then the same power law should apply not only to the estimation of individual sensations, but to sums and differences as well. The experimental evidence in this chapter says ‘Not so’. A variety of ideas have been proposed in attempts to save the role of magnitude estimates as measures of sensation. These include non-extensive ratio-scale measurement, attributing a subjective value to number itself, and a two-stage model for the judgment of the combined sensation of pairs of stimuli presented both simultaneously and successively (the resultant estimates are different). The idea of the power law as a definitive measure of sensation finally founders on certain situations, in the judgment of loudness and of brightness, in which an increase in total stimulus magnitude leads to a reduction in judged sensation.
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