Bayesian Stories: Persuasion, Suggestion, and Mantra

Abstract

We give a predictive-processing account of three phenomena usually treated apart: a rhetorical device from the smoking-cessation literature, the rebound produced by negated instructions, and the contemplative use of mantra. Belief is a precision-weighted posterior. The claim is negative: persuasion and suggestion rarely supply better evidence, and so rarely move a posterior mean. They act instead on the support of a distribution, collapsing it or filling it, or on the precision that weights prior against likelihood. Working in an exponential family, we isolate four generators of belief change, show that translate and reweight move the natural parameter while collapse changes the base measure that carries the support, and prove that bounded evidence can only translate and reweight, never delete. Carr's blank page is the information projection onto the beliefs that vanish on the deleted set, with a Pythagorean cost identity and an irreversibility property. The "no rush" rebound is ironic instantiation, with intrusion increasing in prohibition precision; an appendix derives the monotonicity from precision as gain, and it is the non-commutativity of collapse and fill. Self-hypnosis is offline editing under lowered precision; future pacing is a contraction with a computable stationary law and an Ornstein-Uhlenbeck limit. Mantra realises all three: as iterated pseudo-observation it concentrates a posterior at an explicit rate; as channel occupation it empties one; as serial negation it is a martingale whose limit sits on a non-predicable residual. We give three designs with estimands and a power calculation, and state the limits.