Q3. (Confirmation Bias) Suppose the state space is S = {$1, $2}, where $ stands for...

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Q3. (Confirmation Bias) Suppose the state space is S = {$1, $2}, where $₁ 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(8₁) = 0.8 and p(82) 0.2. Suppose his friend is a (partitional) information source who knows what others think of him, that is, she can confirm whether the state is = 81 or $2. (a) Suppose the friend provides information in the form of the event {$2}. What is the agent's Bayesian posterior conditional on {$2}? (b) Suppose now that the agent is psychologically motivated to maintain his strong belief in what he already believes. He achieves this by doubting the validity of the information he receives: he tells himself that his friend surely twists the truth to protect his feelings. In particular, he believes that if his friend sees s2 then she truthfully reports {s2} but if she sees s₁ then she still reports {s2}. (i) Show that the agent views his friend as a Blackwell experiment. (ii) What is the agent's Bayesian posterior when the friend reports the positive news {$2}? Q3. (Confirmation Bias) Suppose the state space is S = {$1, $2}, where $₁ 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(8₁) = 0.8 and p(82) 0.2. Suppose his friend is a (partitional) information source who knows what others think of him, that is, she can confirm whether the state is = 81 or $2. (a) Suppose the friend provides information in the form of the event {$2}. What is the agent's Bayesian posterior conditional on {$2}? (b) Suppose now that the agent is psychologically motivated to maintain his strong belief in what he already believes. He achieves this by doubting the validity of the information he receives: he tells himself that his friend surely twists the truth to protect his feelings. In particular, he believes that if his friend sees s2 then she truthfully reports {s2} but if she sees s₁ then she still reports {s2}. (i) Show that the agent views his friend as a Blackwell experiment. (ii) What is the agent's Bayesian posterior when the friend reports the positive news {$2}?

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a The agents Bayesian posterior conditional on the event s2 can be calculated using Bayes theorem ps... View the full answer