Carter Blair
Publications
Probably Approximately Consensus: On the Learning Theory of Finding Common Ground
A primary goal of online deliberation platforms is to identify ideas that are broadly agreeable to a community of users through their expressed preferences. Yet, consensus elicitation should ideally extend beyond the specific statements provided by users and should incorporate the relative salience of particular topics. We address this issue by modelling consensus as an interval in a one-dimensional opinion space derived from potentially high-dimensional data via embedding and dimensionality reduction. We define an objective that maximizes expected agreement within a hypothesis interval where the expectation is over an underlying distribution of issues, implicitly taking into account their salience. We propose an efficient Empirical Risk Minimization (ERM) algorithm and establish PAC-learning guarantees. Our initial experiments demonstrate the performance of our algorithm and examine more efficient approaches to identifying optimal consensus regions. We find that through selectively querying users on an existing sample of statements, we can reduce the number of queries needed to a practical number.
Procedural Fairness in Multi-Agent Bandits
In the context of multi-agent multi-armed bandits (MA-MAB), fairness is often reduced to outcomes: maximizing welfare, reducing inequality, or balancing utilities. However, evidence in psychology, economics, and Rawlsian theory suggests that fairness is also about process and who gets a say in the decisions being made. We introduce a new fairness objective, procedural fairness, which provides equal decision-making power for all agents, lies in the core, and provides for proportionality in outcomes. Empirical results confirm that fairness notions based on optimizing for outcomes sacrifice equal voice and representation, while the sacrifice in outcome-based fairness objectives (like equality and utilitarianism) is minimal under procedurally fair policies. We further prove that different fairness notions prioritize fundamentally different and incompatible values, highlighting that fairness requires explicit normative choices. This paper argues that procedural legitimacy deserves greater focus as a fairness objective, and provides a framework for putting procedural fairness into practice.