1. Fig. 1 Experimental and analytic procedure.
Experimental and analytic procedure. (A) Subjects learned the ordering of seven-item lists, consisting of images (A, B, C, etc.). The correct item is always the item that occurs early in the list (e.g., B is correct for the pair BC). (B) Trial structure. After touching a start stimulus, subjects see two images. Touching the correct stimulus yields rewards of varying magnitude. Incorrect responses yield no reward and a brief time-out period. (C) Stimuli were presented in pairs. Training sessions presented only adjacent pairs, outlined in blue. Testing sessions presented all pairs. Reward amounts depended on the rank of the correct stimulus. The “reverse gradient” delivered one drop of water for correct responses to A, two drops for correct responses to B, etc. This gradient is labeled “reverse” because the overall expected value of F exceeds that of E, although choosing F when the EF pair is presented results in no reward. Thus, expected value cannot be used to guide which choice is correct. The “concordant gradient” delivered six drops for correct choices of A, five for B, etc. Therefore, the stimulus with the higher expected value is concordant with the correct choice. (D) Bayesian model for estimating stimulus position from observed response accuracy. Subjects are presumed to make use of a linear representation with uncertain stimulus positions. We assume that this representation takes the form of a normal distribution with some mean and SD for each stimulus. To infer these parameters, we estimated p(correct) for each pair and transformed this to the area above zero of some z distribution. Inferring the parameters in our representation is then done as a simultaneous estimation problem, implemented using Stan. Stimuli adapted from images in the public domain.
Greg Jensen et al. Sci Adv 2019;5:eaaw2089
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