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where the transition from the second to the third line reflects the fact that the sum over h∗h^{*} is the same as the sum over hh in the denominator of Bayes’ rule, so the two terms cancel. As a consequence, after entering their hypothesis h∗h^{*} and receiving data d1d_{1}, the probability that an agent selects a particular hypothesis is exactly the same as before they interacted with the chatbot. By induction, the same result holds across subsequent interactions – the hypothesis an agent enters will be drawn from p(h|d0)p(h|d_{0}) and the process will repeat.
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