Reference no: EM132868218

Question: (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 si or s₂.

(a) Suppose the friend provides information in the form of the event {s₁}. 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 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)?