Polarization in Continuum State Spaces

Determine whether belief polarization—defined as divergence in the first-order stochastic dominance order between the priors and posteriors of two Bayesian agents with distinct full-support priors after observing the same public signal—can occur when the underlying state space is continuous (a continuum) rather than finite and discrete.

Background

Baliga, Hanany, and Klibanoff proved that for Bayesian agents with different priors on a finite one-dimensional state space, observing a common public signal cannot induce polarization in the sense of first-order stochastic dominance. Different examples discussed by Dixit and Weibull involve continuum state spaces but do not fully specify priors, leaving open whether such polarization can occur in continuous settings.

This paper demonstrates that multidimensional polarization is possible on finite product spaces and characterizes when it can persist. However, extending impossibility or possibility results to continuum state spaces remains unresolved. Establishing whether polarization is compatible with Bayesian updating in continuous state spaces would clarify the scope of rational polarization models beyond discrete settings.