Perhaps unsurprisingly, these data reveal that it is challenging to design Bell scenario experiments for cognition where the no signalling condition holds. However, the level of signalling was low enough to meaningfully test for contextuality. In this experiment, no contextuality was found.

The 1 min display time for images employed in the design of the present study was aimed at accessing the Hot system of processing, however, qualitative data revealed evidence that this may have been less a ective than anticipated. Participants appeared to dedicate significant time to their explanation of the reasons behind their decisions to a level of detail that reflects the Cold system of processing. Given that contextuality was assumed to reside in the Hot, more a ective, processing system, a failure to gather answers based purely on this system may have contributed to the small correlations observed.

When conducting Bell scenario designs, the designer must minimize the differences in marginal probabilities in four cases (See Tables 1 and 2). The only way to do this is to choose appropriate stimuli and questions. Despite judicious choices, it often happens that marginal di erences are not minimized in all four cases. The experiment above is yet another example of this. Even when the level of signalling is reduced to meaningfully analyze contextuality ( 0 < 1), the requirement for violating the CHSH inequalities is increased by the condition 2(1 + O ). Moreover, in order to secure violations of the CHSH inequalities, the design must produce strong pair wise (anti-)correlations6 in order to demonstrate the contextuality of the cognitive phenomenon. In previous work [2], we found that the requirement for the experimental design to (1) reduce di erences in marginal probabilities and (2) produce strong correlations can quite easily run counter to each other. These two requirements present a significant challenge for experimenters to uncover contextuality using the Bell scenario design. Perhaps these challenges explain part of the reason why demonstrating contextuality in cognition has thus far been so elusive, notwithstanding [3].

5 Summary and Conclusions

This article documents an empirical pilot study to determine whether decisions of image trustworthiness are contextual. A Bell scenario experimental design was

6Ideally three strong positive correlations and one strong anti-correlation, or the converse.

employed which manipulated both content and representational features from a probabilistic information fusion model in order to minimize the di erence in marginal probabilities across experimental conditions. In addition, participants were subjected to time pressure in order to promote judgments emanating from the Hot system of processing. Qualitative data from a previous study suggested evidence that decisions of image trustworthiness were based on both content and representational features of an image. This opened the door for a Bell scenario design based on content and representational decision subsystems. It was hypothesized that there would be little or no signalling the respective subsystems. In addition, two out of the four image stimuli were selected with an expectation of creating large correlations between content and representational features. Two further image stimuli were selected expecting the correlations to be less as a contrast.

Experimental results did confirm our signalling hypothesis to a degree; although signalling was present, it was at statistically insignificant levels. Experiments with larger sample sizes are needed to further confirm this hypothesis.

CHSH analysis, which takes signalling into account, was performed, and no evidence of contextuality was revealed. The expected strong correlations did not eventuate, possibly due to the fact that the Hot processing system, in which contextuality was expected to occur, was not truly accessed. The study revealed a tension between the requirement for minimizing the di erence in marginal probabilities and the need to produce the strong correlations required to empirically ascertain contextuality. This experiment highlights the challenges in applying Bell scenario designs for investigating contextuality in cognition.

Acknowledgements. This research was supported by the Asian O ce of Aerospace Research and Development (AOARD) grant: FA2386-17-1-4016 and the InterPARES Trust (https://interparestrust.org). Thanks to Abdul Obeid for his technical support.

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