Contextuality in Collective Intelligence: Not There Yet

Type I contextuality or inconsistent connectedness is a fundamental feature of both the classical as well as the quantum realms. Type II contextuality (true contextuality or CHSH type contextuality) is frequently asserted to be specific to the quantum realm. Nevertheless, evidence for Type II contextuality in classical settings is slowly emerging (at least in the psychological realm). An example is given here of Type II contextuality involving a simple cooperative game. This arises due to the cooperative nature of the game which results in sign intransitivity for expectation values while individual random variables remain consistently connected. This shows that the conditions attributed uniquely to quantum systems may occur in classical settings as well. Sign intransitivity can be observed in preference relations in the setting of decision making and so intransitivity in decision making may also yield examples of Type II contextuality. Previously it was suggested that a fruitful setting in which to search for such contextuality is that of decision making by collective intelligence systems. An experiment was conducted using a detailed simulation of nest emigration by workers of the ant Temnothorax albipennis. In spite of intransitivity, these simulated colonies came close to but failed to violate Dzhafarov’s inequality for a 4-cyclic system. Further research using more sophisticated simulations and experimental paradigms is required