Skip to main content

Quantum Decision Making

Periodic Reporting for period 1 - QDM (Quantum Decision Making)

Reporting period: 2016-10-01 to 2018-09-30

The objectives concerned how people update their beliefs given new information and, relatedly, the process of rumination/ ambivalence towards reaching a ‘complex’ decision (i.e. a decision for which there is no clear answer and which is based on several pieces of information). Together with collecting relevant human experimental results, we also aimed to develop models based on quantum probability theory (QPT). We call QPT the rules for probability assignment from quantum mechanics, without the physics. QPT is in principle applicable in any area where there is a need to formalize uncertainty. In psychology, quantum-like cognitive models have been fruitfully employed, especially in situations that challenge the predominant descriptive (and normative) framework of classical probability theory (CPT). Such situations have been extremely influential in the development of our understanding of human decision making (e.g. they have led to two Nobel prizes, to Kahneman and Thaler).

Regarding the first major project objective, belief updating, there is a striking difference between belief updating based on CPT and QPT. With the former, belief updating is constrained by Bayes law, so that initially unlikely hypotheses are unlikely to be supported too much, regardless of the evidence that comes to light. With the latter, belief updating can involve large jumps from prior to posterior beliefs. Does human decision making sometimes involve such large jumps? Regarding the second major project objective, we often have an intuitive sense of rumination, such that we go back and forth the possible alternatives before reaching a decision. How can we empirically measure such a process and how can we model it?
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).
The predominant frameworks for understanding decision making have been CPT and, where there appears discrepancy between CPT and behaviour, individual heuristics and biases. Quantum-like cognitive models have been providing a third, major alternative theoretical direction: on several occasions, they have allowed formalization of behaviours which have so far been the remit of heuristics and biases, thus enabling new predictions and insights into the underlying cognitive processes. The research within this project has provided two sets of empirical results which further challenge the scope of applicability of traditional formalisms, regarding belief updating and rumination. We observed belief updating which involves probability changes too large to be consistent with CPT, thus challenging the status of CPT as the predominant framework for understanding belief change, and rumination patterns involving multiple cycles, thus posing difficulties for current dynamical approaches. We also showed that QPT models could describe these results. Our modelling represents one of the first instances of a quantum-like cognitive models employing open systems, which is significant both regarding the technical enhancements incorporated for open systems (ours is one of the first such applications in cognition) and the detailed fit for experimental results.

Non-academic impact is already promising. We have been in touch with the BBC in the UK, regarding the application of a quantum-like framework to understand persistent disagreement in modern politics. We have also been discussing applications with the (American) Office of Naval Research Global, with a view to apply quantum-like principles for modelling cooperation between multiple agents.