  Information diffusion on social networks has been described as a collective
outcome of threshold behaviors in the framework of threshold models. However,
since the existing models do not take into account individuals' optimization
problem, it remains an open question what dynamics emerge in the diffusion
process when individuals face multiple (and possibly incompatible) information.
Here, we develop a microfounded general threshold model that enables us to
analyze the collective dynamics of individual behavior in the propagation of
multiple information. The analysis reveals that the virality of competing
information is fundamentally indeterminate. When individuals maximize
coordination with neighbors, the diffusion process is described as a saddle
path, thereby leading to an unpredictable symmetry breaking. When individuals'
choices are irreversible, there is a continuum of stable equilibria where a
certain degree of social polarization takes place by chance.
