A rejection mechanism in 2D bounded confidence provides more conformity

This paper explores the dynamics of attitude change in two dimensions resulting from social interaction. We add a rejection mechanism into the 2D bounded confidence (BC) model proposed by Deffuant et al. (2001). Individuals are characterized by two-dimensional continuous attitudes, each associated with an uncertainty u, supposed constant in this first study. Individuals interact through random pairs. If their attitudes are closer than u on both dimensions, or further than u on both dimensions, or closer than u on one dimension and not further than u + delta u on the other dimension, then the rules of the BC model apply. But if their attitudes are closer than u on one dimension and further than u + delta u on the other dimension, then the individuals are in a dissonant state. They tend to solve this problem by shifting away their close attitudes. The model shows metastable clusters, which maintain themselves through opposite influences of competitor clusters. Our analysis and first experiments support the hypothesis that, for a large range of uncertainty values, the number of clusters grows linearly with the inverse of the uncertainty, whereas this growth is quadratic in the BC model.