Group consensus under asymmetric voting behavior

In this study, we propose a group formation model by assuming voters hold asymmetric irrationality, namely the probability of accepting a candidate with whom they disagree with. Moreover, we utilize a non-Markovian function by introducing a rationality decay rate to represent that agents' rationality decays as their contributed admissions on the candidate increase. We have systematically explored the impact of non-Markovian asymmetric irrationality, voter selection mechanisms, voter number, and group size on the degree of consensus. Our findings indicate that, with only one voter, as the group size increases, the degree of consensus converges to a value determined by the irrationality ratio. Remarkably, even in scenarios with significant asymmetry in irrationality, a substantial degree of consensus can still be maintained. Furthermore, for multiple voters, the relationship between the degree of group consensus and rationality decay rate exhibits non-monotonic behaviors. In summary, this research offers new theoretical insights into group dynamics and provides implications for enhancing consensus in real-world social groups.