Ian Kash

Rafael Frongillo, Ian Kash, Mary Monroe

Peer prediction mechanisms are typically proposed and analyzed under the assumption that the report and signal spaces are identical. In practice, however, agents often observe richer information which they then map to a coarser report space. Motivated by this discrepancy between theory and practice, we initiate the study of peer prediction mechanisms with signal spaces that are richer than the report space. We begin by formalizing a model with real-valued signals and binary reports. In this setting, it is natural to study symmetric threshold strategies, where agents map their signals to binary reports according to a single real-valued threshold. For several well-known binary-report peer prediction mechanisms, we show that most equilibria under the original assumption of binary signals are no longer equilibria in our model. Furthermore, dynamic analysis proves that some of the remaining thresholds are unstable. These results extend beyond real-valued signals and binary reports to settings where the signal space is finer-grained than the report space. While the results above suggest important limitations for the deployment of existing peer prediction mechanisms in practice, we also use them to develop a new, more robust mechanism. This mechanism generates a larger number of stable threshold equilibria under our model, thus allowing the designer more flexibility in choosing how agents map their signals to reports.

Jack Blandin, Ian Kash

Group fairness definitions such as Demographic Parity and Equal Opportunity make assumptions about the underlying decision-problem that restrict them to classification problems. Prior work has translated these definitions to other machine learning environments, such as unsupervised learning and reinforcement learning, by implementing their closest mathematical equivalent. As a result, there are numerous bespoke interpretations of these definitions. Instead, we provide a generalized set of group fairness definitions that unambiguously extend to all machine learning environments while still retaining their original fairness notions. We derive two fairness principles that enable such a generalized framework. First, our framework measures outcomes in terms of utilities, rather than predictions, and does so for both the decision-algorithm and the individual. Second, our framework considers counterfactual outcomes, rather than just observed outcomes, thus preventing loopholes where fairness criteria are satisfied through self-fulfilling prophecies. We provide concrete examples of how our counterfactual utility fairness framework resolves known fairness issues in classification, clustering, and reinforcement learning problems. We also show that many of the bespoke interpretations of Demographic Parity and Equal Opportunity fit nicely as special cases of our framework.