Eliciting Predictions and Recommendations for Decision Making YILING CHEN, Harvard University

When making a decision, a decision maker selects one of several possible actions and hopes to achieve a desirable outcome. To make a better decision, the decision maker often asks experts for advice. In this article, we consider two methods of acquiring advice for decision making. We begin with a method where one or more experts predict the effect of each action and the decision maker then selects an action based on the predictions. We characterize strictly proper decision making, where experts have an incentive to accurately reveal their beliefs about the outcome of each action. However, strictly proper decision making requires the decision maker use a completely mixed strategy to choose an action. To address this limitation, we consider a second method where the decision maker asks a single expert to recommend an action. We show that it is possible to elicit the decision maker’s most preferred action for a broad class of preferences of the decision maker, including when the decision maker is an expected value maximizer

Prediction Markets: Theory and Applications

In this thesis I offer new results on how we can acquire, reward, and use accurate predictions of future events. Some of these results are entirely theoretical, improving our understanding of strictly proper scoring rules (Chapter 3), and expanding strict properness to include cost functions (Chapter 4). Others are more practical, like developing a practical cost function for the [0, 1] interval (Chapter 5), exploring how to design simple and informative prediction markets (Chapter 6), and using predictions to make decisions (Chapter 7).Engineering and Applied Science

Algorithmic Bayesian Epistemology

One aspect of the algorithmic lens in theoretical computer science is a view on other scientific disciplines that focuses on satisfactory solutions that adhere to real-world constraints, as opposed to solutions that would be optimal ignoring such constraints. The algorithmic lens has provided a unique and important perspective on many academic fields, including molecular biology, ecology, neuroscience, quantum physics, economics, and social science. This thesis applies the algorithmic lens to Bayesian epistemology. Traditional Bayesian epistemology provides a comprehensive framework for how an individual's beliefs should evolve upon receiving new information. However, these methods typically assume an exhaustive model of such information, including the correlation structure between different pieces of evidence. In reality, individuals might lack such an exhaustive model, while still needing to form beliefs. Beyond such informational constraints, an individual may be bounded by limited computation, or by limited communication with agents that have access to information, or by the strategic behavior of such agents. Even when these restrictions prevent the formation of a *perfectly* accurate belief, arriving at a *reasonably* accurate belief remains crucial. In this thesis, we establish fundamental possibility and impossibility results about belief formation under a variety of restrictions, and lay the groundwork for further exploration

Designing informative securities

We create a formal framework for the design of informative securities in prediction markets. These securities allow a market organizer to infer the likelihood of events of interest as well as if he knew all of the traders’ private signals. We consider the design of markets that are always informative, markets that are informative for a particular signal structure of the participants, and informative markets constructed from a restricted selection of securities. We find that to achieve informativeness, it can be necessary to allow participants to express information that may not be directly of interest to the market organizer, and that understanding the participants’ signal structure is important for designing informative prediction markets.