Persistent mixed worldviews in the theory of chosen preferences

Bernheim, Braghieri, Mart\'inez-Marquina, and Zuckerman (2021, American Economic Review) develop a theory of chosen preferences and conjecture convergence to pure worldviews at low mindset flexibility. We show that the (original) conjecture fails: with arbitrarily many worldviews, a common-value action sustains mixed worldviews in every stationary equilibrium from a relatively open set of initial worldviews, even when all pure worldviews are absorbing. However, finite linear programs characterize a sufficient persistence condition. Conversely, mixed accumulation points require shared valuation maxima. If each implementable action has a unique maximizing evaluator, every existing stationary equilibrium converges to purity for all interior flexibility and discount parameters. Experienced utility converges without uniqueness. In existing equilibria, small payoff perturbations preserve compromise over fixed horizons with high probability. Strictly tailored worldviews yield existence and a one-step equilibrium characterization at sufficiently low mindset flexibility; weak implementation can preclude stationary pure-strategy existence. The persistence and convergence results extend to stationary randomization.