Scale convergence as a criterion for rescaling: Information integration with difference, ratio, and averaging tasks

Ss lifted pairs of weights simultaneously, one in each hand, and judged either the difference, ratio, or average heaviness of the two weights. Data for the difference and ratio tasks were in general agreement with subtractive and ratio models, but the averaging data showed discrepancies from the constant-weight averaging model similar to those reported in previous psychophysical research. Rescaling was ruled out for the averaging data, because responses to pairs of equal weight were a linear function of subtractive model scale values derived from the difference task data. Scale values for the ratio and difference task data were related exponentially, as were the responses to the pairs, consistent with Torgerson’s conjecture that Ss do not distinguish “differences” from “ratios.” They appear to use the same composition rule but different output functions, depending on the procedures for responding. The scale convergence criterion can thus prevent inappropriate rescaling when a model fails and can dictate rescaling even when a model fits.