Judging ratio increases and decreases: ignoring asymmetric sensitivity

People frequently judge the consequences of percentage increases and decreases in ratios, such as changes in speed, productivity, and energy efficiency. Prior research has shown that people often treat nonlinear ratio relationships as linear. The current research examines an important directional implication of this tendency. In inverse ratios, equal percentage increases and decreases do not have equally large consequences: a decrease produces a larger effect than an equivalent increase. People tend to neglect this asymmetry and instead respond as if increases and decreases have equal but opposite effects. Consequently, when judgments concern the quantity inversely related to the ratio, people underestimate the consequences of ratio decreases and overestimate those of ratio increases. Across four preregistered studies of judgments about driving speed, productivity, and environmental ratios, participants were highly accurate when the judgement target was linearly related to the ratio but exhibited systematic directional bias when it was inversely related. These findings extend previous accounts of linear reasoning by identifying a systematic directional consequence of neglecting the asymmetric sensitivity of inverse ratio changes.