  In this article, we relax the Bayesianity assumption in the now-traditional
model of Bayesian Persuasion introduced by Kamenica & Gentzkow. Unlike
preexisting approaches -- which have tackled the possibility of the receiver
(Bob) being non-Bayesian by considering that his thought process is not
Bayesian yet known to the sender (Alice), possibly up to a parameter -- we let
Alice merely assume that Bob behaves 'almost like' a Bayesian agent, in some
sense, without resorting to any specific model.
  Under this assumption, we study Alice's strategy when both utilities are
quadratic and the prior is isotropic. We show that, contrary to the Bayesian
case, Alice's optimal response may not be linear anymore. This fact is
unfortunate as linear policies remain the only ones for which the induced
belief distribution is known. What is more, evaluating linear policies proves
difficult except in particular cases, let alone finding an optimal one.
Nonetheless, we derive bounds that prove linear policies are near-optimal and
allow Alice to compute a near-optimal linear policy numerically. With this
solution in hand, we show that Alice shares less information with Bob as he
departs more from Bayesianity, much to his detriment.
