This dissertation consists of three essays in microeconomic theory. The first two focus on how to elicit information about the state of the world from strategic agents, either to make a decision or for its own sake. The third studies a model of decentralized two-sided matching markets.
In "Mechanisms for making accurate decisions in biased crowds," I study decision rules for finding the true answer to a binary question using the opinions of biased agents. Taking majority rule as a baseline, I study peer-prediction decision rules, which ask agents to predict the opinions of others in addition to providing their own. Incorporating first-order beliefs into the decision rule has the potential to recognize the correct answer even when the majority is wrong. However, I show the majority rule is essentially the only deterministic, neutral, anonymous, and interim dominance solvable mechanism. I then characterize all randomized peer-prediction mechanisms with these properties, using this result to show majority rule is the optimal mechanism in this class. Finally, I consider a simple, non-incentive-compatible decision rule based on the median prediction that implements majority rule when all agents are strategic and improves on majority rule when an unknown subpopulation is honest.
In "Minimum truth serums with optional predictions," I introduce a class of mechanisms for eliciting private correlated signals from a group of expected score maximizers without external verification or knowledge about the agents' belief structure. Built on proper scoring rules, these minimum truth serums ask agents to report a signal and a prediction of the signals of others. If two agents with the same signal have the same expectations about the signals of others, the Bayesian incentive compatibility of these mechanisms follows with no further assumptions on the agents' belief structure. With a slight modification, the mechanism is still feasible and incentive compatible when the prediction portion of the report is optional.
In "Uncoordinated two-sided matching markets," I study a decentralized proposal model in joint work with Juan Fung. The study of two-sided matching markets is now a major subfield of market design, focused primarily on the variants of the deferred acceptance algorithm. As a centralized mechanism, deferred acceptance is guaranteed to return a stable match. However, there is little definite work on whether uncoordinated agents find a stable matching on their own and the consequences if not. We show that small to moderately large uncoordinated markets reach a stable match within n^2 proposals from each agent when the proposal strategy isn't completely naive. We also show that stopping the proposal process early before stabilizing results in a more egalitarian and higher welfare match, particular when the two sides of the market are unbalanced. This suggests uncoordinated markets wouldn't benefit from centralization unless there is an obvious failing like market unraveling
