The size-weight illusion and beyond: A new model of perceived weight.

In the size-weight illusion (SWI), the smaller of two same-weight, same apparent material objects is perceived as heavier. The SWI has proved difficult to explain via traditional Bayesian models, which predict the opposite effect: expected weight from size (smaller = lighter) should be integrated with felt weight, such that the smaller object should be perceptually lighter. Other authors have proposed that weight and density are combined according to Bayesian principles, or that Bayesian models incorporating efficient coding can predict the SWI via 'likelihood repulsion'. These models, however, have been evaluated only under the narrow conditions of typical SWI stimuli. Here we establish a general model of perceived weight for pairs of objects that differ in weight and/or density and/or size by varying amounts. In a visuo-haptic task, participants (N = 30) grasped and lifted pairs of cubes, and reported their perceived heaviness. We report that the SWI occurs even at very small density differences, repudiating the idea that the illusion requires a large difference between expected and felt weight. Across all object pairs, perceived weight was well described by a model (R2 = .98) that includes a positive influence of both objects' weights and the judged object's density, but a negative influence of the other object's density. Critically, the influence of both densities on perceived weight is strongly modulated by weight difference, being three times as large for zero/small weight differences than for large differences. Thus, it is only under the unusual conditions of typical SWI studies that density affects perceived weight to a substantial extent. Unlike existing models, that are inconsistent with our more comprehensive dataset, our descriptive model provides a quantitative, accurate and generalised account of weight perception for pairs of objects across various weight and size conditions.