agent’s Bayesian posterior condition on $2

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Q3. (Confirmation Bias) Suppose the state space is S = S1, S2, where
si 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(s) = 0.8
and p(82) = 0.2. Suppose her friend is a (partitional) information source who
knows what others think of her and can confirm whether the state is $ı or $2.
(a) Suppose the friend provides information in the form of the event $2.
What is the agent’s Bayesian posterior condition on $2?
(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
$2 then he truthfully reports S2 but if he sees sų 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?

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