Eliciting and Aggregating Information: An Information Theoretic Approach

Crowdsourcing---outsourcing tasks to a crowd of workers (e.g. Amazon Mechanical Turk, peer grading for massive open online courseware (MOOCs), scholarly peer review, and Yahoo answers)---is a fast, cheap, and effective method for performing simple tasks even at large scales. Two central problems in this area are: Information Elicitation: how to design reward systems that incentivize high quality feedback from agents; and Information Aggregation: how to aggregate the collected feedback to obtain a high quality forecast. This thesis shows that the combination of game theory, information theory, and learning theory can bring a unified framework to both of the central problems in crowdsourcing area. This thesis builds a natural connection between information elicitation and information aggregation, distills the essence of eliciting and aggregating information to the design of proper information measurements and applies the information measurements to both the central problems: In the setting where information cannot be verified, this thesis proposes a simple yet powerful information theoretical framework, the emph{Mutual Information Paradigm (MIP)}, for information elicitation mechanisms. The framework pays every agent a measure of mutual information between her signal and a peer's signal. The mutual information measurement is required to have the key property that any ``data processing'' on the two random variables will decrease the mutual information between them. We identify such information measures that generalize Shannon mutual information. MIP overcomes the two main challenges in information elicitation without verification: (1) how to incentivize effort and avoid agents colluding to report random or identical responses (2) how to motivate agents who believe they are in the minority to report truthfully. To elicit expertise without verification, this thesis also defines a natural model for this setting based on the assumption that emph{more sophisticated agents know the beliefs of less sophisticated agents} and extends MIP to a mechanism design framework, the emph{Hierarchical Mutual Information Paradigm (HMIP)}, for this setting. Aided by the information measures and the frameworks, this thesis (1) designs several novel information elicitation mechanisms (e.g. the disagreement mechanism, the $f$-mutual information mechanism, the multi-hierarchical mutual information mechanism, the common ground mechanism) in various of settings such that honesty and efforts are incentivized and expertise is identified; (2) addresses an important unsupervised learning problem---co-training by reducing it to an information elicitation problem---forecast elicitation without verification.PHDComputer Science & EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/145809/1/yuqkong_1.pd