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Essays in Non-Bayesian Information Transmission

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This dissertation studies interactions between a non-Bayesian decision maker (DM) and a sophisticated information provider who wants to influence the DM. In the essay ``Strategic Justifications," an auditor receives a justification from a self-interested expert who wants to convince the auditor that she acted in good faith for her clients. The auditor verifies if the proposed justification is coherent with the observed data. If the justification is not coherent, the auditor severely punishes the expert. I explore to what extent this requirement of providing coherent justifications to an auditor, who may lack expertise, aligns the interests of the expert and her clients. The essay ``Choosing Sample Sizes" considers a DM who receives information about a payoff-relevant parameter in the form of samples. This essay asks: How large a sample would a designer provide to a DM in order to convince the DM that the parameter value is sufficiently high? It solves for the designer's optimal sample sizes when the DM is a frequentist or a Bayesian statistician, and data are Bernoulli experiments governed by the parameter value.

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