Perceptual Control Theory Model of the “Beads in the jar” task Tristan Robert Browne (tristan.browne@postgrad.manchester.ac.uk ) Faculty of Life Sciences, University of Manchester, Oxford Road, Manchester, M13 9PL, UK Warren Mansell (warren.mansell@manchester.ac.uk ) School of Psychological Sciences, University of Manchester, M13 9PL, UK Wael El-Deredy (wael.el-deredy@manchester.ac.uk ) School of Psychological Sciences, University of Manchester, M13 9PL, UK Keywords: PCT; DTD; Hierarchical control. Introduction Perceptual Control Theory (hereafter PCT) has been successfully employed in modelling skilled performance (Marken, 2001) and prescribing errors (Marken, 2003). Here we model the draws-to-decision (DTD) behaviour of participants on the “beads-in-the-jar” task (see Fine et al., 2007). PCT is a control theory approach to explaining human behaviour, derived from negative-feedback loops used in engineering and developed for the application to Psychology since the latter half of the last century (Powers, 1973). The theory states that all behaviour is purposeful and is intended to control specific environmental variables. A system of hierarchical control directs behaviour through interconnected control systems at multiple levels. Higher level systems set reference values for immediately subservient systems and these systems also feedback information regarding their current state. First order systems act on, perceive and feedback the state of the controlled variable to the system hierarchy. “Beads in the jar task” Participants were told there were two jars, (jar R 60:40 red to green and jar G 60:40 green to red beads) and that up to 20 beads would be drawn randomly from one of the jars, with a 50% chance of either jar being chosen. The task required subjects to choose after the first draw and on every subsequent draw either which jar the beads were coming from or to draw another bead. They were instructed only to decide when they were sure which jar the beads were coming from. The number of draws participants chose before deciding was the draws-to-decision (DTD) measure. Method Behavioural data was collected from 39 participants in the “beads-in-the-jar” task under three conditions: High Cost Condition (HCC) where participants could win £4 by deciding the correct jar on the first draw, and then lost 20p for every subsequent draw; Low Cost Condition (LCC) initial winnings £2 on the first draw and then 10p lost for every draw; and the No Cost Condition (NCC) where no winnings or drawing costs were applied. Participants’ mean DTD was significantly lower in the HCC than in the two other conditions, and significantly lower in the LCC than the NCC (figure 1). Figure 1: Mean conditional DTDs and associated standard error. Significant differences found between all conditions. Model Our PCT model of the DTD behaviour employed two competing control systems at the same level: 1) participants were controlling for how much drawing was costing, 2) participants perceived how sure they were of which jar the beads were being drawn from. This fed into a comparator that outputted a decision when they were surer of it being jar R or jar G than how much they perceived it cost them to draw another bead. We modelled these using winnings versus the perceived likelihood of the jars (exp. 1) and perceived total cost versus jar uncertainties (exp. 2). Results Experiment.1 We accounted for all possible DTD results in the HCC and the 18/20 LCC using a perceived likelihood measure based on red and green bead counts and optimising the gain on the winnings only using a deterministic linear optimisation for each DTD value (equations.1-3). 0 2 4 6 8 10 12 14 16 High Cost Low Cost No Cost Mean Draws-to-Decision Experimental Condition