A mass-density model can account for the size-weight illusion.

When judging the heaviness of two objects with equal mass, people perceive the smaller and denser of the two as being heavier. Despite the large number of theories, covering bottom-up and top-down approaches, none of them can fully account for all aspects of this size-weight illusion and thus for human heaviness perception. Here we propose a new maximum-likelihood estimation model which describes the illusion as the weighted average of two heaviness estimates with correlated noise: One estimate derived from the object's mass, and the other from the object's density, with estimates' weights based on their relative reliabilities. While information about mass can directly be perceived, information about density will in some cases first have to be derived from mass and volume. However, according to our model at the crucial perceptual level, heaviness judgments will be biased by the objects' density, not by its size. In two magnitude estimation experiments, we tested model predictions for the visual and the haptic size-weight illusion. Participants lifted objects which varied in mass and density. We additionally varied the reliability of the density estimate by varying the quality of either visual (Experiment 1) or haptic (Experiment 2) volume information. As predicted, with increasing quality of volume information, heaviness judgments were increasingly biased towards the object's density: Objects of the same density were perceived as more similar and big objects were perceived as increasingly lighter than small (denser) objects of the same mass. This perceived difference increased with an increasing difference in density. In an additional two-alternative forced choice heaviness experiment, we replicated that the illusion strength increased with the quality of volume information (Experiment 3). Overall, the results highly corroborate our model, which seems promising as a starting point for a unifying framework for the size-weight illusion and human heaviness perception.