(Confirmation Bias) Suppose the state space is S = {s1, s2}, where s1 stands for "people think ill of me" and s2 stands for "people think well of me". Due to a negative way of looking at the world, the agent has beliefs p(s1) = 0.8 and p(s2) = 0.2. Suppose her friend is a (partitional) information source who knows what others think of her and can confirm whether the state is s1 or s2.

(a) Suppose the friend provides information in the form of the event {s2}. What is the agent's Bayesian posterior condition on {s2}?

(b) Suppose now that the agent is psychologically motivated to maintain her strong belief in what she already believes. She achieves this by doubting the 1 validity of her information: she tells herself that the friend surely twists the truth to protect her feelings. In particular, she believes that if her friend sees s2 then he truthfully reports {s2} but if he sees s1 then he still reports {s2}. (i) Show that the agent views her friend as a Blackwell experiment. (ii) What is the agent's Bayesian posterior when the friend reports the positive news {s2}?