Schematic depiction of the Betasort algorithm’s representation of position

(A) Each stimulus has an associated beta distribution, whose parameters encode both the stimulus position and its uncertainty. In order to choose between available options, the algorithm draws a value for each possibility, then chooses the item whose random draw yielded the highest value. Additionally, there is a probability ρ of the subject ignoring these values and making a response at random. (B) Following a choice, the representation is updated. The first stage of updating is “relaxation,” which increases the uncertainty of the estimated position without changing the means of any of the distributions. This applies to all items, regardless of whether the stimuli were present during that trial or not. (C) If the subject makes a correct choice, then the distributions for all items are consolidated (again, whether or not any given stimulus was presented). What subject make consistently correct responses, the relaxation and consolidation steps effectively balance one another out. (D) If, however, the subject makes an incorrect choice, then updating proceeds in two stages. During direct updating, the means of the stimuli presented during that trial are moved apart to reduce the odds of another erroneous response. (E) The preceding step is them immediately followed by incorrect updating of all stimuli that were not visible during the trial. Stimuli that were between the two items are consolidated, items whose current mean lies below that of the pair are shifted further downward, and pairs whose mean lies above the pair are shifted upward