  When opinions, behaviors or ideas diffuse within a population, some are
invariably stickier than others. The stickier the opinion, behavior or idea,
the greater is an individual's inertia to replace it with an alternative. Here
we study the effect of stickiness of opinions in a two-opinion model, where
individuals change their opinion only after a certain number of consecutive
encounters with the alternative opinion. Assuming that one opinion has a fixed
stickiness, we investigate how the critical size of the competing opinion
required to tip over the entire population varies as a function of the
competing opinion's stickiness. We analyze this scenario for the case of a
complete-graph topology through simulations, and through a semi-analytical
approach which yields an upper bound for the critical minority size. We present
analogous simulation results for the case of the Erd\H{o}s-R\'enyi random
network. Finally, we investigate the coarsening properties of sticky opinion
spreading on two-dimensional lattices, and show that the presence of stickiness
gives rise to an effective surface tension that causes the coarsening behavior
to become curvature-driven.
