Regarding the project strand corresponding to belief updating, we developed an experimental paradigm based on a suspect situation. Briefly, a theft was committed, there were various suspects such that initially participants would be guided to consider some as likely, some as unlikely, and finally some surprising new evidence came to light, such that it drastically altered initial expectations regarding guilt. Participants had to provide probability ratings regarding guilt before and after the new evidence. We then attempted to model the probability updating with both CPT and QPT. We showed that the CPT rule for updating could not accommodate the size of change from prior to posterior probabilities, but the QPT rule could. Note, in some cases there was evidence for zero prior probabilities, that is, the probability of guilt for some suspects was considered to be zero. This is significant, because according to CPT a zero prior probability cannot update (the name for this phenomenon is Cromwell’s paradox). We outlined a descriptive QPT model for the observed probabilities. The main result from this work is that naïve human observers can readily produce probabilities which violate CPT constraints and QPT can provide a formal framework for understanding these probabilities.
Regarding the project strand corresponding to rumination, we created scenarios for which the hypothetical protagonists were faced with a complex decision (e.g. how to spend their Friday evening), with multiple, non-matched pros and cons for each of the two decision outcomes. Participants were asked to consider this information and reach a decision. We developed two ways to measure the extent of rumination. First, we employed a technology called mouse-tracking, which keeps track of mouse movements. By using a presentation format which allowed viewing of the arguments for each decision outcome only when the mouse moved in different screen regions, we could measure how participants drifted across different sets of arguments. Second, with collaborators in Germany and Switzerland, we created an eye tracking version of the experiment, such that we continuously tracked eye fixations as participants considered the available information. The latter provided a richer data set, which we have modelled with a QPT framework for dynamical change. An innovative aspect of this framework is that it incorporates open system dynamics. In QPT, dynamical change with open system dynamics is characteristic of situations where the system interacts with its environment. Psychologically, such situations are ones for which the consideration of a problem is not restricted to problem-specific information, but is also influenced by the general knowledge/ experience of the decision maker. Our main results were that in many cases participants’ deliberation shows evidence of rumination (multiple cycles concerning the consideration of one set of arguments vs. the other) and that the dynamical pattern of rumination was also consistent with oscillation followed by stabilization – this latter characteristic indicates open-system dynamics. We provided a sophisticated open-systems QTP model for these results, showing that the dynamics of QPT (including the open systems elaboration) provide a good framework for modelling rumination. A notable aspect of the QPT model fits was that, in some cases, QPT model parameters could be employed to predict the eventual participant decision. This is a significant finding, since it is surprising that eye tracking structure can be related to decisions (only the gaze cascade effect has provided any indication that this might be the case so far).
