Measurement and the mental map

In order to test between subtractive and ratio theories of stimulus comparison, judges were asked to estimate “ratios” and “differences” of easterliness and westerliness of U.S. cities. “Difference” judgments fit the subtractive model, and “ratio” judgments fit the ratio model. However, “ratios” and “differences” were monotonically related, contrary to the theory that judges compute both relations on a common scale. Results are consistent with the theory that there is but one operation for both “ratios” and “differences.” To assume that the single operation is a ratio requires the complex interpretation that easterliness and westerliness are nonlinearly related. A simpler interpretation is provided by a subtractive theory, in which all four types of judgments are monotonically related to subjective differences on a single cognitive map.