DELIBERATION, LEARNING CONDITIONAL PROBABILITY, AND RISK: THREE ESSAYS

Abstract

This dissertation investigates how rational inquiry and decision-making depend on the structure of information, evidence, and risk. Across three chapters, I examine how individuals or groups update their beliefs, communicate what they learn, and choose under uncertainty.Chapter 1, “Deliberation Under Dynamic Discovery of Evidence,” develops a model of group deliberation in which evidence discovery is dynamic: agents are more likely to uncover high-quality evidence when their current beliefs are closer to the truth. Using computer simulations, I compare different practices of communicating evidence and conclusions. The results show that communication about evidence is most valuable when agents can access good evidence, since it enables groups to pool and accumulate information. By contrast, when high-quality evidence is difficult to obtain, communication about conclusions can be more effective, allowing agents to benefit from others’ relatively successful inquiries. More generally, extensive communication of conclusions usually improves collective performance, whereas extensive communication of evidence is not always beneficial. The optimal communication strategy depends on how difficult the scenario is. Chapter 2, “A Bayesian Reflection on the Judy Benjamin Problem,” addresses the Judy Benjamin problem and argues that it is under-specified. Bayesian conditioning on learned conditional probabilities requires an extended probability space, but the original story does not determine a unique such space. Models with different extended spaces, therefore, yield different posterior beliefs. I argue that these competing models reflect different structural representations of Judy’s situation, and that accuracy considerations can choose among them only when the case is supplemented with further facts about the actual structure of Judy’s situation. Chapter 3, “A Calibration Theorem for Risk-Weighted Expected Utility Theory” establishes a calibration theorem for risk-weighted expected utility theory (REU). REU is intuitively appealing as it seems to resolve some of the classical challenges to EU, such as the Allais paradox and Rabin’s calibration result. I calibrate REU using Allais preferences. Thus, REU resolves the Allais paradox only at the cost of becoming susceptible to a Rabin-style challenge (being calibratable). Compared to existing calibration results against REU, my approach relies on less demanding and more realistic assumptions.