Deciding by quantum-like belief morphing or hopping?Its application to multi-agent response influence

Other people’s beliefs may influence our own. Such effects, sometimes referred to as ‘crowd-wisdom’, can be revealed from group-informed responses in controlled experiments. Our study presents a formal choice model to understand how multiple respondents iteratively interact when communicating their responses, which we test on data from Granovskiy et al. (2015)’s social information experiment. In this multi-stage decision process, information from the group’s response distribution influences individual judgments before respondents adjust their next response. Our model describes each respondent’s probabilistic belief state, and uses a quantum-like morphing evolution based on the Brassard–Høyer–Grover amplification formalism. This framework enables: (i) the description of multi-respondent cognitive interactions through assimilation to or polarization away from other beliefs, (ii) the implementation via Hamiltonian operators using projection operators of source (‘initial’) and target (‘informing’) belief states, and (iii) the resolution of periodicity issues in previous Schrödinger-like models through bounded temporal parametrization. A performance comparison is done for the quantum-like models using morphing and standard hopping, and a classical Markov hopping model. The quantum-like morphing model with a multi-component target belief demonstrated superior BIC performance across the parameter space of evolution time ( t frac ), belief uncertainty (SD), and sampling temperature ( T ). This belief morphing approach hence provides an effective and innovative method to model social influence in group decision-making.