Approaching consensus can be delicate when positions harden (Q1083127)

The purpose of this paper is to show by examples that, when experts harden their positions, a very small change in the process of weighting other experts' estimates can divert the process from moving toward consensus almost surely to remaining in dissension almost surely, or vice versa. The model leads to the study of the ergodic behavior of a product of random nonnegative matrices which, as it turns out, may depend discontinuously on a continuous parameter. In these examples a nonstationary product of random matrices changes from being weakly ergodic with probability 1 to being weakly ergodic with probability 0 as a parameter of the process changes smoothly.