  The arise of disagreement is an emergent phenomenon that can be observed
within a growing social group and, beyond a certain threshold, can lead to
group fragmentation. To better understand how disagreement emerges, we
introduce an analytically tractable model of group formation where individuals
have multidimensional binary opinions and the group grows through a noisy
homophily principle, i.e., like-minded individuals attract each other with
exceptions occurring with some small probability. Assuming that the level of
disagreement is correlated with the number of different opinions coexisting
within the group, we find analytically and numerically that in growing groups
disagreement emerges spontaneously regardless of how small the noise in the
system is. Moreover, for groups of infinite size, fragmentation is inevitable.
We also show that the model outcomes are robust under different group growth
mechanisms.

Physics and Society