Eliciting and Aggregating Truthful and Noisy Information

In the modern world, making informed decisions requires obtaining and aggregating relevant information about events of interest. For many political, business, and entertainment events, the information of interest only exists as opinions, beliefs, and judgments of dispersed individuals, and we can only get a complete picture by putting the separate pieces of information together. Thus, an important first step towards decision making is motivating the individuals to reveal their private information and coalescing the separate pieces of information together. In this dissertation, I study three information elicitation and aggregation methods, prediction markets, peer prediction mechanisms, and adaptive polling, using both theoretical and applied approaches. These methods mainly di↵er by their assumptions on the participants’ behavior, namely whether the participants possess noisy or perfect information and whether they strategically decide on what information to reveal. The first two methods, prediction markets and peer prediction mechanisms, assume that the participants are strategic and have perfect information. Their primary goal is to use carefully designed monetary rewards to incentivize the participants to truthfully reveal their private information. As a result, my studies of these methods focus on understanding to what extent are these methods incentive compatible in theory and in practice. The last method, adaptive polling, assumes that the participants are not strategic and have noisy information. In this case, our goal is to accurately and e ciently estimate the latent ground truth given the noisy information, and we aim to evaluate whether this goal can be achieved by using this method experimentally. iii I make four main contributions in this dissertation. First, I theoretically analyze how the participants’ knowledge of one another’s private information a↵ects their strategic behavior when trading in a prediction market with a finite number of participants. Each participant may trade multiple times in the market, and hence may have an incentive to withhold or misreport his information in order to mislead other participants and capitalize on their mistakes. When the participants’ private information is unconditionally independent, we show that the participants reveal their information as late as possible at any equilibrium, which is arguably the worse outcome for the purpose of information aggregation. We also provide insights on the equilibria of such prediction markets when the participants’ private information is both conditionally and unconditionally dependent given the outcome of the event. Second, I theoretically analyze the participants’ strategic behavior in a prediction market when a participant has outside incentives to manipulate the market probability. The presence of such outside incentives would seem to damage the information aggregation in the market. Surprisingly, when the existence of such incentives is certain and common knowledge, we show that there exist separating equilibria where all the participants’ private information is revealed and fully aggregated into the market probability. Although there also exist pooling equilibria with information loss, we prove that certain separating equilibria are more desirable than many pooling equilibria because the separating equilibria satisfy domination based belief refinements, maximize the social welfare of the setting, or maximize either participant’s total expected payo↵. When the existence of the outside incentives is uncertain, trust cannot be established and the separating equilibria no longer exist. Third, I experimentally investigate participants’ behavior towards the peer prediction mechanisms, which were proposed to elicit information without observable ground truth. While peer prediction mechanisms promise to elicit truthful information by rewarding participants with carefully constructed payments, they also admit uninformative equilibria where coordinating participants provide no useful information. We conduct the first controlled