Empirical evaluation of the axioms of multiplicativity, commutativity, and monotonicity in ratio production of area

Although direct scaling methods have been widely used in the behavioral sciences since the 1950s, theoretical approaches which could clarify the implicit assumptions inherent in Stevens' ratio scaling approach were developed only recently. Today, it is generally accepted that the axioms of commutativity and multiplicativity are fundamental to the subjects' ratio scaling behavior. Therefore, both axioms were evaluated in ratio production of area. Participants were required to adjust the area of a variable circle to prescribed ratio production factors. The results are in accordance with previous empirical findings: commutativity was satisfied, whereas multiplicativity failed to hold. Additionally, the validity of the monotonicity property was analyzed, which postulates that the subjects' adjustments in a ratio production experiment preserve the mathematical order of the ratio production factors. Monotonicity was satisfied empirically, which is consistent with all the current theories of ratio scaling.