Eliciting and Aggregating Information for Better Decision Making

In this thesis, we consider two classes of problems where algorithms are increasingly used to make, or assist in making, a wide range of decisions. The first class of problems we consider is the allocation of jointly owned resources among a group of agents, and the second is the elicitation and aggregation of probabilistic forecasts from agents regarding future events. Solutions to these problems must trade off between many competing objectives including economic efficiency, fairness between participants, and strategic concerns.

In the first part of the thesis, we consider shared resource allocation, where we relax two common assumptions in the fair divison literature. Firstly, we relax the assumption that goods are private, meaning that they must be allocated to only a single agent, and introduce a more general public decision making model. This allows us to incorporate ideas and techniques from fair division to define novel fairness notions in the public decisions setting. Second, we relax the assumption that decisions are made offline, and instead consider online decisions. In this setting, we are forced to make decisions based on limited information, while seeking to retain fairness and game-theoretic desiderata.

In the second part of the thesis, we consider the design of mechanisms for forecasting. We first consider a tradeoff between several desirable properties for wagering mechanisms, showing that the properties of Pareto efficiency, incentive compatibility, budget balance, and individual rationality are incompatible with one another. We propose two compromise solutions by relaxing either Pareto efficiency or incentive compatibility. Next, we consider the design of decentralized prediction markets, which are defined by the lack of any single trusted authority. As a consequence, markets must be closed by popular vote amongst a group of anonymous, untrusted arbiters. We design a mechanism that incentivizes arbiters to truthfully report their information even when they have a (possibly conflicting) stake in the market themselves.